Question

What is the simplest form of x^4y^7/ 3√x^10y^4?

A. xy^6
B. x^9y^9
C. x^8y^9 3√x^2y^2
D. y^5 3√x^2y^2

Answer 1

D. y^5 ^3sqrtx^2y^2

Explanation:

Got it right on edge

Answer 2

x^4y^7/ (x^10y^4)^1/3

power to a power means multiply

x^4y^7/ (x^(10*1/3)y^(4*1/3)

x^4y^7/ (x^(10/3)y^(4/3)

exponents divided by exponents means subtract the exponents

x^(4-10/3) y^(7-4/3)

x^(12/3-10/3) y^(21/3 - 4/3)

x^ (2/3) y^ (17/3)

x^ (2/3) y^ (5 2/3)

x^ (2/3) y^ (5 +2/3)

exponents added are the terms multiplied

(x^ 2/3 y^ 5 y ^ 2/3)

y^ 5 (x^ 2/3 y ^ 2/3)

we can take the 1/3 back out

y^5 ( x^2 y^2) ^ 1/3

Choice D