Which Expression Equals SAT Question

SATboi

I have an SAT practice question stating: Which of the following expressions is equivalent to (-4x^3)^2/3?

The answer is 2x^2 * 3âˆš2 (or ^2/3, I don't know how to indicate that specifically using keys but the 3 is inside the v of the square root symbol)

But my question is how I would multiply that expression to get the answer? Any math calculator or guide I consult seems to say that you can't multiply the expression, but it's clearly happening here.

Thank you very much!

skipjack

Forum Staff
If x is real, $\left(-4x^3\right)\!^{2/3} = \left(-2^2\!\left(x^3\right)\right)\!^{2/3} = \left((-2)^{4/3}\right)\!x^2 = 2\!\left(2^{1/3}\right)\!x^2 = 2\sqrt[\large3]{2}x^2\!$.

EvanJ

To show my work without using fractional exponents as much, take the square and then the cube root. The square is 16x^6. To simplify, write it as 2*8x^6. The cube root of 8 is the first part of skipjack's answer, the cube root of 2 is the second part of his answer, and the cube root of x^6 is x^2.