Exponential Form Conversion

Question

Does $(\sqrt[3]{3k})^4 = (3k)^{4/3}$ or $((3k)^{1/3})^4$?

I thought the first one is correct, but when I looked at it again I saw that $(3k)^{4/3} = \sqrt[3]{(3k)^4} $

If it says in my instructions to put it in exponential form, which one should I write as my final answer? — , Aug 26 '14 at 17:30
I would think the second one (since it's in the form of $(3k)^{\text{exponent }}$. But you might ask for clarification to be sure. — Semiclassical, Aug 26 '14 at 17:31

score 2 · Accepted Answer · answered Aug 26 '14 at 17:34

2

All forms are equivalent.

By definition

$\sqrt[3]{3k} = (3k)^{1/3}$

and the exponents multiply:

$((3k)^{1/3})^4 = (3k)^{1/3 \times 4} = (3k)^{4/3}$

answered Aug 26 '14 at 17:34

Null

1 Answers1