Question

Which expression is equivalent to StartRoot 8 x Superscript 7 Baseline y Superscript 8 Baseline EndRoot? Assume x greater-than-or-equal-to 0.
x y squared StartRoot 8 x cubed EndRoot
2 x cubed y cubed StartRoot x y squared EndRoot
2 x cubed y Superscript 4 Baseline StartRoot 2 x EndRoot
4 x cubed y Superscript 4 Baseline StartRoot x EndRoot

Answer 1

sqrt(8 x^7 y^8) = sqrt(8)·sqrt(x^7)·sqrt(y^8)
= 2√2 · x^3√x · y^4
= 2 x^3 y^4 √(2x).

So the equivalent expression is: 2 x^3 y^4 √(2x) (choice 3).