Question

Can someone tell me how to simplify 32 to the 3/4 power? I don't need the answer, just steps.

Answer 1

\[\sqrt[4]{32^3} = \sqrt[4]{32768}\]

Answer 2

\(32^{3/4} = \left(2^{5}\right)^{3/4} = 2^{5\cdot (3/4)} = 2^{15/4} = 2^{[(12/4) + (3/4)]} = 2^{12/4}\cdot 2^{3/4} = 2^{3}\cdot 2^{3/4} = 8\cdot 2^{3/4}\)

There are shorter paths, but I liked that one.

Answer 3

@Elizabeth_Christine Are you supposed to leave your answer in simplified radical form or simplified exponential form?