Question

Select all radical expressions that are equivalent to 4^3/5 .

3√4^5

5√64

5√4^3

(3√4)^5

5√12

3√20

Answer 1

remember

$x^ \frac{m}{n} = \sqrt[n]{x^m}$
and
$(x^m)^n=x^{mn}$
 so

$x^ \frac{3}{5} = \sqrt[5]{4^3}$
but wait, there's more

4=2², so

$x^ \frac{3}{5} = \sqrt[5]{4^3} = \sqrt[5]{(2^2)^3} = \sqrt[5]{2^6}$=
$2^ \frac{6}{5}=(2^ \frac{5}{5})(2^ \frac{1}{5})=2 \sqrt[5]{2}$

also, 4^3=64


so possible ones are
$2^ \frac{6}{5}$
$\sqrt[5]{4^3}$
$\sqrt[5]{64}$
$2 \sqrt[5]{2}$
of the ones listed, the 2nd and 3rd options are correct ($\sqrt[5]{4^3}$ and $\sqrt[5]{64}$)

Answer 2

The 2nd and 3rd are correct