An example of a rational function is y = (3x²+7x+4)/(x²+3x+2) which has a horizontal asymptote at y = 3.
To give it a horizontal asymptote of y = 3, we require the degrees in the numerator and denominator to be and the lead coefficient ratio to be 1.
Yet, in producing the hole, we need to have the rest of the function, disregarding the (x + 1)'s, = 1 when x = -1 to ensure the y-value of the hole is at + 1. When we add all of this together, we get.
y = (3(x+1)(x+k))/((x+1)(x+2)) and the last condition requires k = + 4/3, so
By distributing the 3 in the numerator to the 2nd linear component, we get.
y = (3(x+1)(x+4/3))/((x+1)(x+2))
y = ((x+1)(3x+4))/((x+1)(x+2))
y = (3x²+7x+4)/(x²+3x+2)
Thus, the example of a rational function is y = (3x²+7x+4)/(x²+3x+2) which has a horizontal asymptote at y = 3.
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Which of the following equations shows how substitution can be used to solve the following system of equations?
By substituting the first equation into the second, we get:
2x + 5*(2x +3) = 3
The correct option is the second one.
Which equation shows how substitution?Here we have the system of equations:
y = 2x + 3
2x + 5y = 3
You can see that the variable "y" is already isolated in the first equation, so we can just substitute it in the second equation:
2x + 5*(2x +3) = 3
This is what we can see in the second option, so we conclude that the second option is the correct one.
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please help !! if anyone knows
Answer:
Answer down below!
Step-by-step explanation:
We can tell from ABC and A'B'C' that they are similar, but not alike
Segment AC = 6 and segment A'C' =4
They just subtracted two from the 6
Let's do the same thing for segment BC!
If BC = 3, then we know that B'C' = 1
if you placed $5 into an account that paid interest at a rate of 5%, and compounded interest yearly, how much would that account be worth in 100 years
After adding interest the sum would be worth $657.51 .
Interest is the amount paid over and above the original amount to a lender or depositor by a borrower or deposit-taking financial institution at a predetermined rate in the domains of finance and economics (the amount borrowed).
Interest differs from any fees the borrower may be required to pay to the lender or another party.interest also contrasts from a dividend, which is cash distributed to shareholders (owners) by a corporation from its profit or reserve, but not at a predefined rate or proportionally; rather, it is a portion of the reward or interest gained by risk-taking businessmen when revenue is made that surpasses all expenditures.Interest when the principal is $5 , time is 100 years and rate is 5%.
We know that from compound interest:
Amount = principal (1 + rate)ⁿ
Therefore
Amount = 5 (1 +0.05)¹⁰⁰
Amount = $657.5062...
Amount ≈ $657.51
Therefore adding interest the sum would be worth $657.51
5. Realizar las siguientes operaciones y simplificar el resultado:
a. 3(x3 − x2 + 5) − 8(x3 − 4x2 + 7x)
b. 7x2 + 2x + 5 + x(x + 7)
c. 10 (t3 − 4t2 + 1) − t(2t + 6) + 8(t3 − t − 5)
d. (x − 1)(x + 2)(x − 3)
e. (3a − 2b2)(3a + 2b2) − 3(4a − b2)2 + 2(−2a − b2)(2a − b2)
Answer:
a. -5x³ + 29x² - 56x + 15
b. 8x² + 9x + 5
c. 18t³ - 42t² - 14t - 30
d. x³ - 2x² - 5x + 6
e. -2b⁴ + a² + 6b² - 24a
Step-by-step explanation:
a. 3(x³ − x² + 5) − 8(x³ − 4x² + 7x)
3x³ - 3x² + 15 - 8x³ + 32x² - 56x
-5x³ + 29x² - 56x + 15
b. 7x² + 2x + 5 + x(x + 7)
7x² + 2x + 5 + x² + 7x
8x² + 9x + 5
c. 10(t³ − 4t² + 1) − t(2t + 6) + 8(t³ − t − 5)
10t³ - 40t² + 10 - 2t² - 6t + 8t³ - 8t - 40
18t³ - 42t² - 14t - 30
d. (x − 1)(x + 2)(x − 3)
(x - 1)(x + 2)
x(x + 2) - 1(x + 2)
x² + 2x - x - 2
x² + x - 2(x - 3)
x(x² + x - 2) - 3(x² + x - 2)
x³ + x² - 2x - 3x² - 3x + 6
x³ - 2x² - 5x + 6
e. (3a − 2b²)(3a + 2b²) − 3(4a − b²)2 + 2(−2a − b²)(2a − b²)
3a(3a - 2b²) + 2b²(3a - 2b²)
9a² - 6ab² + 6ab² - 4b⁴ - 3(4a − b²)2 + 2(−2a − b²)(2a − b²)
9a² - 4b⁴ - 24a + 6b² + 2(−2a − b²)(2a − b²)
(−2a − b²)(2a − b²)
-2a(2a - b²) - b²(2a - b²)
-4a² + 2ab² - 2ab² + b⁴
-4a² + b⁴
2(-4a² + b⁴)
-8a² + 2b⁴
9a² - 4b⁴ - 24a + 6b² - 8a² + 2b⁴
-2b⁴ + a² + 6b² - 24a
Put the following equation of a line into slope-intercept form, simplifying all fractions. 3y-2x= -9
y=2/3x-3 that is the slope intercept form
plsssssss helppppp meee with this
Answer:
Step-by-step explanation:
Answer:
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Step-by-step explanation:
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Jonathan has 3982 stickers in his sticker collection. Jessie has 2825 stickers in his collection. How many stickers do Jonathan and Jessie have altogether?
Daniel and Paul have saved $37 to buy their mother a present Daniel saved $8 less than paul how much money did Paul save a ) 14.75b) 18.50c)20.00d)22.50
Answer:
D. 22.50
Step-by-step explanation:
22.5 - 8 = 14.5
14.5 + 22.5 = 37
Some people advise that in very cold weather, you should keep the gas tank in your car more than half full. Lou's car had 16.2 gallons in the 15 gallons in the -gallon tank on the coldest day of the year.
Lou filled the tank with gas that cost $ 3.50 per gallon. How much did Lou spend on gas?
From the given parameter, the total amount that Lou spent on the gas is; $30.8
How to solve Algebra Word Problems?We are told that Lou's car had 6.2 gallons in the 15 gallons in the -gallon tank on the coldest day of the year.
Now, Lou filled the tank with gas that cost $ 3.50 per gallon.
Thus;
Amount of gas that Lou bought = 15 - 6.2
Amount of gas that Lou bought = 8.8 gallons
Since he bought these gallons at the cost of $3.50 per gallon, then it means that;
Total amount he spent = 8.8 * 3.5
Total amount he spent = $30.8
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Complete question is;
Some people advise that in very cold weather, you should keep the gas tank in your car more than half full. Some people advise that in very cold weather, you should keep the gas tank in your car more than half full. Lou's car had 6.2 gallons in the 15 gallons in the -gallon tank on the coldest day of the year.
Lou filled the tank with gas that cost $ 3.50 per gallon. How much did Lou spend on gas?
can someone pls explain to me how to find y intercept
Answer:
(0, -5)
Explanation:
The function is represented by f(x), and the line graphed would be y= f(x). In slope-intercept form, the equation of a line is given by y= mx +c, where m is the slope and c is the y-intercept.
Since we know that the line is linear, any two points along the line would give us the same slope value. Since y-intercepts occur at x= 0, let the y-intercept be (0, y).
[tex]\boxed{ \text{slope} = \frac{y _{1} - y_2 }{x_1 - x_2} }[/tex]
Slope between (-3, 1) and (1, -7)= slope between (-3, 1) and (0, y)
[tex] \frac{1 - ( -7 )}{ - 3 - 1} = \frac{y - 1}{0 - ( - 3)} [/tex]
[tex] \frac{1 + 7}{ - 4} = \frac{y - 1}{0 + 3} [/tex]
[tex] \frac{8}{ - 4} = \frac{y - 1}{3} [/tex]
[tex] - 2 = \frac{y - 1}{3} [/tex]
Multiply both sides by 3:
-2(3)= y- 1
-6= y -1
Add 1 to both sides:
y= -6 +1
y= -5
Thus, the y-intercept is (0, -5).
__________
Based on the image, however, we are to find the equation of the linear function in slope-intercept form.
The first step would be to find the slope between any two points, which would be -2. This is found using the slope formula, and we have calculated it above.
Substitute the value of the slope into y= mx +c:
y= -2x +c
The y-intercept can be found by substituting a pair of coordinates the line passes through.
When x= -3, y= 1,
1= -2(-3) +c
1= 6 +c
c= 1 -6
c= 5
Thus, the equation of the line is y= -2x +5.
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Answer:
y = - 2x - 5
The intercept is 5 because that is where the graph cuts the y axis.
PLEASE MARK AS BRAINLIEST IF YOU FOUND IT HELPFUL BECAUSE IT MAKES ME FEEL GOOD!
Step-by-step explanation:
Linear Standard Formy = mx + c;
The m equals the change in y divided by the change in x. If you choose left to right for y then you must do the same for x as well.
Δy = ( - 7 ) - ( - 15 ); Δx = 1 - 5;
Δy = - 7 + 15;
Δy = 8;
Δx = - 4;
m = 8 / - 4;
m = - 2;
y = - 2x + c;
Point SubstitutionPick a point (x, y) and sub it into the equation. Make sure to use brackets when subbing.
- 7 = - 2( 1 ) + c;
- 7 = - 2 + c;
Add 2 to both sides.
- 7 + 2 = - 2 + 2 + c;
- 5 = c;
c = - 5;
The c is the intercept.
y = - 2x - 5
A total of 77 tornadoes have been documented in tuscaloosa county in the period beginning on january 1, 1950 and ending on december 31, 2020. What is the recurrence interval for tornadoes in tuscaloosa county?.
The number of tornadoes is 77
total time for occurrence is 70 years
using these
= ( 77/70)
= ( 1.1 )
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PLEASE HURRY I NEED HELP RIGHT NOW!!
What is the length of BC?
Answer:
31cm
Step-by-step explanation:
Add AC and BC together to get AB.
AC = 2x - 13 and
BC = 3x + 4 and
AB = 36 (this is all the given information)
The two smaller pieces can be combined to equal the whole segment.
AC + BC = AB
2x - 13 + 3x + 4 = 36
combine like terms.
5x - 9 = 36
Add 9
5x = 45
Divide by 5.
x = 9
But you're not done because they asked for BC.
BC = 3x + 4
substitute 9 for x.
BC = 3(9) + 4
BC = 27 + 4
BC = 31
BC is 31 cm.
the greatest common divisor of two integers is $(x 2)$ and their least common multiple is $x(x 2)$, where $x$ is a positive integer. if one of the integers is 24, what is the smallest possible value of the other one?
The greatest common divisor (24,6) is 6 and the least common multiple (24,6) is 24.
As per the question statement, the greatest common divisor of two integers is (x+2) and the least common multiple x(x+2). It is given that one of the integers is 24.
Let us assume that "b" is the value of other one.
greatest common divisor(24,b) = (x+2)
least common multiple(24,b) = x(x+2)
Formula:
greatest common divisor(24,b)*least common multiple(24,b) = 24*b
24*b = (x+2)*x(x+2)
[tex]b = \frac{x(x+2)^{2} }{24} \\[/tex]
Hence, the smallest possible value of the other one is "6" and x = 4.
Hence, the greatest common divisor (24,6) is 6 and the least common multiple (24,6) is 24.
Common divisor: A number or expression that evenly divides two or more other numbers or phrases.Common multiple: A number into which every number in a particular collection may be split equally.To learn more about common divisor and common multiple, click on the link given below:
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The Transverse Tire Company produces all types of tires at its factory. Due to fixed costs associated with the running of
the factory, the company starts with a loss of $200,000, or a profit of -$200,000, at the beginning of each month. The
first major hurdle the company faces each month is to break even, or reach a the point at which the profit is zero. The
company sells tires in batches of 1000. it earns $40,000 for each batch of tires it manufactures and sells.
1. Identify the two quantities that are changing in this situation.
2. identify the independent and dependent variables for these quantities.
3. Write an equation to represent the profit the company will make when they manufacture and sell batches of tires.
4. Use your equation to complete the table for this situation:
5. What is the unit rate of change in this problem?
please help i need to submit but today
The solutions for each statement are given below.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
The initial amount of the company = -$200,000
Earnings for selling one batch = $40,000
Now,
1.
The two quantities that are changing in this situation are:
The number of batches.
The amount of profit.
2.
The independent variable is the number of batches.
The dependent variable is the profit.
3
The number of batches = x
The amount of profit = y
The equation for the profit.
P = -200,000 + B x 40,000
Where B is the number of batches.
4.
Batches of tires Profits
B P
0 -200,000
1 -160,000
2 -120,000
3 -80,000
4 -40,000
5 0
5.
The unit rate of change.
= (-120,000 + 160,000) / (2 - 1)
= 40,000
Thus,
The statements are given above.
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The table shows values of f(x). What is the value of f(2)? Enter your answer in the box. f(2)=
X: 0 1 2 3 4
f(x): 4 2 3 9 1
According to the table, the value of the function f(2) is 3
What are functions?Functions are equations, ordered pairs, tables and graphs that are used to represent a relation
How to evaluate the function?From the question, the function is represented by the table of values given as
X: 0 1 2 3 4
f(x): 4 2 3 9 1
From the question, the function to calculate is given as
f(2)
This means that we calculate the value of the function, when x = 2
i.e.
We calculate f(x), when x = 2
So, we look at the table of values for this function value
From the table of values, we have
When x = 2, f(x) = 3
This means that
f(2) = 3
So, we can conclude that the value of the function f(2) based on the given table when x =2 is 3
Hence, the function f(2) has a value of 3
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Ralph Kansky was hired as an administrative assistant for Hereford Cattle Company. His annual salary is $98,280. What is his weekly salary?
Answer:
u shall simply divide 98290 by 365 bc there are 365 days in 1 year
Step-by-step explanation:
98280 divided by 365 and that makes..
a restaurant offers three desserts, and exactly twice as many appetizers as main courses. a dinner consists of an appetizer, a main course, and a dessert. what is the least number of main courses that the restaurant should offer so that a customer could have a different dinner each night in the year 2003?
The least number of main courses that the restaurant should offer is 8.
What is linear inequality ?The mathematical expression with unequal sides is known as an inequality in mathematics. Inequality is referred to in mathematics when a relationship results in a non-equal comparison between two expressions or two numbers. In this instance, any of the inequality symbols, such as greater than symbol (>), less than symbol (), greater than or equal to symbol (), less than or equal to symbol (), or not equal to symbol (), is used in place of the equal sign "=" in the expression. Polynomial inequality, rational inequality, and absolute value inequality are the various types of inequalities that can exist in mathematics.
Calculationslet m be the number of main courses restaurant serves
so, 2m is the number of appetizers
then the number of dinner combination is = 2m x m x 3 = 6m^2
since the customer wants to eat a different dinner in all 365 days of 2003,
we must have ,
[tex]6m^{2}[/tex] ≥ 365
[tex]m^{2}[/tex] ≥ 60.83.....
also the 2003 is not a leap year
because 2003 / 4 is not equal to an integer
the smallest integer value satisfies this is 8 .
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3) Graph the solution set to y - 2x = -5 on the
coordinate plane.
Answer:
y=2x-5
Step-by-step explanation:
y - 2x = -5
add 2x to both sides.
y=-5+2x
Answer:
y = 2x - 5 is a line. determine the two points that this line intersects with the axes then connect these points to graph it.
Step-by-step explanation:
Given y = 2x -5 set y = 0 then solve for the abscissa
y = 2x - 5
0 =2x - 5
2x=5
x = 5/2
we now have the point (5/2,0)
set now x = 0 then solve for ordinate
y = 2x - 5
y = 2(0) - 5
y = -5
we now have the point (0, - 5)
we now simply draw a line passing thru the two points ( 5/2, 0) and (0, - 5)
kindly see the graph of y = 2x - 5 with points (5/2, 0) and (0, - 5)
Hope this helps
A recipe of chicken marinade says mix 3 parts with oil with 2 parts soy sauce and 1 part orange juice if you need 42 cups of marinade in all how much of each ingredient should you use
Answer:
21 cups oil
14 cups soy sauce
7 cups orange juice
Step-by-step explanation:
Use 1 cup for 1 part. The original recipe as given with its small amounts would make a total of 3 + 2 + 1 = 6 parts, or 6 cups of sauce.
You want to make 42 cups.
42/6 = 7
The amount you want to make is 7 times the amounts in the ratio.
3 parts oil: 3 × 7 = 21: 21 cups oil
2 parts soy sauce: 2 × 7 = 14: 14 cups soy sauce
1 part orange juice: 1 × 7 = 7: 7 cups orange juice
Check: 21 + 14 + 7 = 42
The amounts above do make 42 cups in total.
Answer:
21 cups oil
14 cups soy sauce
7 cups orange juice
Find the value of x in each case:
The angle x has a measure of 37
What are angles?Angles are formed when two or more lines intersect. This in other words means that angles is the measure of space between the intersection of rays or lines
How to determine the value of x?The given parameter is the figure
On the figure, we have the following angle measures
2x, 79, 32 and 5x
The sum of angles in a quadrilateral is 360 degrees
So, we have the following equation
2x + 79 + 32 + 360 - 5x = 360
Evaluate the like terms in the above equation
So, we have the following equation
-3x + 79 + 32 = 0
Evaluate the like terms in the above equation
So, we have the following equation
-3x = -111
Divide both sides of the equation by 3
x = 37
Hence, the value of x is 37
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4 times 10 by the power8 subtract 9times 10 by the 7
Answer:
310000000
That’s the answer
Solve for p
1.5m+3p=18
please show steps
Answer:
Step-by-step explanation:
Answer: p= 6-0.5
solve 1.5m + 3p=18
p= 6-0.5m
Rule 1: Add 3 starting from 0. Rule 2: Add 9 starting from 0. Complete the first 5 terms using the rules. How are the corresponding terms related?
Given the following question:
Rule one: + 3
Rude two: + 9
3, 6, 9, 12, 15
3 + 3 = 6 + 3 = 9
9 + 3 = 12 + 3 = 15
= 15
9, 18, 27, 36, 45
9 + 9 = 18 + 9 = 27
27 + 9 = 36 + 9 = 45
= 45
We are now given..
3, 6, 9, 12, 15
9, 18, 27, 36, 45
They are related because these terms also have a rule, if you mutlply 3, by 3 we get 9, if we multiply 6 by 3 we get 18. The second sequence is three times the corresponding term in the first sequence or the first option.
Your answer is the first option.
help me please if you can:)
In the polygon, The triangles are not similar
What is similar triangles ?The term similar triangles refers to triangles that the ratio of the sides are equal.
In the problem, the sides of the triangles are given as
In DQRS: QR = 4 RS = 15, and < DR = 36In DUVT: VT = 8 TU = 32, and < DT = 36The ratio of the sides
In DQRS: QR / RS = 4/15 = 0.27
In DUVT: VT / TU = 8/32 = 0.25
0.27 ≠ 0.25
since the ratio of the sides are not equal the two triangles are not similar
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Subtract -6x+3om -6x+8.
The difference of the given expressions is 5.
The given expressions are -6x+3 and -6x+8.
What is the subtraction of expressions?To subtract an algebraic expression from another, we should change the signs (from '+' to '-' or from '-' to '+') of all the terms of the expression which is to be subtracted and then the two expressions are added.
Now, subtract -6x+3 from -6x+8
-6x+8 - (-6x+3)
= -6x+8+6x-3
= 5
Therefore, the difference of the given expressions is 5.
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The value of y is directly proportional to the value of x. When x=3.5, the value of y is 14. What is the value of y when x = 28? Record your answer
For x = 28, the value of [y] such that [x] is directly proportional to [y] will be 112.
What is direct proportionality?Direct proportion or direct variation is the relation between two quantities where the ratio of the two is equal to a constant value. Mathematically, direct proportionality is represented by a straight line and it equation is of the form -
y = kx
k = y/x
where [k] is the constant
Given is the value of [y], which is directly proportional to the value of [x], and when [x] = 3.5, the value of [y] is 14.
We have the following data -
[y] = 14 at [x] = 3.5
Now, since [y] is directly proportional to [x], we cam write -
y = kx
k = y/x
k = 14/3.5. [1]
Now, for x = 28, we can write the relation as -
y/x = k
k = y/28 [2]
Now, equating equation [1] and [2], we get -
14/3.5 = y/28
y = (14 x 28)/3.5
y = (140 x 28)/35
y = (140 x 4)/5
y = 28 x 4
y = 112
Therefore, for x = 28, the value of [y] such that [x] is directly proportional to [y] will be 112.
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The value of [tex]\sqrt{6}[/tex] is not -4 because ______.
The solution of the value is mathematically given as
√6 =2.449
This is further explained below.
What is square Root?Generally, In mathematics, the term "square root" refers to a component of a number that, when multiplied by itself, results in the same value as the original number.
As an example, both 3 and –3 are square roots of the number 9.
A number y is said to have a square that is equal to a given number x if and only if it satisfies the following condition: y2 = x.
Another way to express this is to say that the number y has the same value as its own square. For example, the square roots of 16 are 4 and -4, since 42 divided by 2 is 16.
In conclusion,
√6 is not -4
because
√6 =2.449
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there are two aircraft carriers, a and b, and carrier a is longer in length than the carrier b. the total length of these two carriers is feet, while the difference of their lengths is only feet.
there are two aircraft carriers, a and b, and carrier a is longer in length than the carrier b. then Carrier A is 2,104 feet and Carrier B is 2,094 feet.
Since there are two aircraft carriers, A and B, and carrier A is longer in length than the carrier B, and the total length of these two carriers is 4198 feet, while the difference of their lengths is only 10 feet, to determine the length of each aircraft carrier, the following calculation must be performed:
(4,198 - 10) / 2 = X
4.188 / 2 = X
2,094 = X
2,094 + 10 = 2,104
2,094 + 2,104 = 4,198
Therefore, Carrier A is 2,104 feet and Carrier B is 2,094 feet.
the complete question is
There are two aircraft carriers, A and B, and carrier A is longer in length than the carrier B. The total length of these two carriers is 4198 feet, while the difference of their lengths is only 10 feet.
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write an equation in slope intercept form for a horizontal line through (15,21)
Slope-intercept form is y = 21.
What is a equation of line?The equation y = mx + c is the general equation of any straight line where m is the gradient of the line (how steep the line is) and c is the y -intercept (the point in which the line crosses the y -axis).
Given that,
The line is horizontal. It means slope of this line is zero. We can use the point-slope form for a linear equation since we know the slope and the point (15, 21).
Point-slope form: [tex](y-y_{1}) = m(x-x_{1})[/tex]
Where,
m = slope and [tex](x_{1}, y_{1})[/tex] is the points.
Then,
[tex](y-y_{1}) = m(x-x_{1})[/tex]
[tex](y-21) = 0(x-15)[/tex]
[tex]y-21 = 0\\y=21[/tex]
Hence, the Slope-intercept form is y = 21.
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Question 5:
Write an equivalent expression for (15³)4
Answer:
[tex]15^{12}[/tex]
Step-by-step explanation:
assuming you mean
[tex](15^3)^{4}[/tex]
using the rule of exponents
[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex] , then
[tex](15^3)^{4}[/tex]
= [tex]15^{3(4)}[/tex]
= [tex]15^{12}[/tex]