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

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

rx and sx

step-by-step explanation: