The expression with a rational exponent of the seventh root of x to the third power is x to the three sevenths power ⇒ answer A
Step-by-step explanation:
Let us explain how to change the radical expression as an expression
with a rational exponent
1. Find the number of the root and make it the denominator of the
fraction exponent
2. Find the power of the term under the radical and make it the
numerator of the fraction exponent
Examples:

![\sqrt[3]{x^{n}}=x^{\frac{n}{3}}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%5E%7Bn%7D%7D%3Dx%5E%7B%5Cfrac%7Bn%7D%7B3%7D%7D)
![\sqrt[5]{x^{n}}=x^{\frac{n}{5}}](https://tex.z-dn.net/?f=%5Csqrt%5B5%5D%7Bx%5E%7Bn%7D%7D%3Dx%5E%7B%5Cfrac%7Bn%7D%7B5%7D%7D)
So ![\sqrt[m]{x^{n}}=x^{\frac{n}{m}}](https://tex.z-dn.net/?f=%5Csqrt%5Bm%5D%7Bx%5E%7Bn%7D%7D%3Dx%5E%7B%5Cfrac%7Bn%7D%7Bm%7D%7D)
∵ the radical expression is the seventh root of x to the third power
∵ seventh root = ![\sqrt[7]{}](https://tex.z-dn.net/?f=%5Csqrt%5B7%5D%7B%7D)
∵ x to the third power = x³
∴ seventh root of x to the third power = ![\sqrt[7]{x^{3}}](https://tex.z-dn.net/?f=%5Csqrt%5B7%5D%7Bx%5E%7B3%7D%7D)
Let us change it to the rational exponent
∵ ![\sqrt[m]{x^{n}}=x^{\frac{n}{m}}](https://tex.z-dn.net/?f=%5Csqrt%5Bm%5D%7Bx%5E%7Bn%7D%7D%3Dx%5E%7B%5Cfrac%7Bn%7D%7Bm%7D%7D)
∵ ![\sqrt[7]{x^{3}}](https://tex.z-dn.net/?f=%5Csqrt%5B7%5D%7Bx%5E%7B3%7D%7D)
∴ m = 7 and n = 3
∴
= 
∵
is x to the three sevenths power
∴
is x to the three sevenths power
The expression with a rational exponent of the seventh root of x to the third power is x to the three sevenths power
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You can learn more about radical equation is brainly.com/question/7153188
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Answer:
The solution is x=1,y=2,z=3
Step-by-step explanation:
The given system of equations is ;\
2x−3y+4z=8...(1)
3x+4y−5z=−4...(2)
4x−5y+6z=12...(3)
Make x the subject in equation (1)

Put equation (4) into equation (2) and (3)

Multiply through by;

Expand;

Simplify;

Equation (4) in (3)





Put equation (6) into equation (5)




z=3
Put z=3 into equation (6)
y=2(3)-4=2
Put y=2 and z=3 into equation 4

The solution is x=1,y=2,z=3
Six hundred thousand ,+ Eighty thousand ,+ ten.
Answer:
-4 is the average rate of change from 3 to 4
Step-by-step explanation:
Average rate of change is defined as the fraction of change in f(x) value to change in x value.
Here we have x values as 3 and 4.
To find the average rate of change from x=3 to x=4
Average rate of change = change in f(x)/change in x
f(4) = -5^{4-3} +2 = -3\\f(3) = 1\\f(4)-f(3) = -3-1 =-4
Change in x = 4-3 =1