How do you simplify (2x^2 times y^4) to the 3/2 power?

Question

I am rusty onmy Algebra II and this is a problem I have on a review quiz for Calculus I

Thank you,  D. McClure

Answer 1

(2x²y⁴)^3/2=2^3/2x^2×3/2y^4×3/2=√8(x³y⁶). What does 2^3/2 actually mean? Well, we could write it as (2³)^½, because 3×½=3/2. But 2³=2×2×2=8. And raising anything to the power of ½ is the same as finding the square root. So 8^½=√8.

Another way to work out 2^3/2 is to write it as 2^1½=2¹2^½=2√2.

√8=√(2²×2)=(√2²)(√2)=2√2, so the answer is (2x²y⁴)^3/2=2√2x³y⁶.