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

The 2nd and 3rd are correct

Answer 2

remember


`x^ (m)/(n) = \sqrt[n]{x^m}`
and

`(x^m)^n=x^(mn)`
so


`x^ (3)/(5) = \sqrt[5]{4^3}`
but wait, there's more

4=2², so


`x^ (3)/(5) = \sqrt[5]{4^3} = \sqrt[5]{(2^2)^3} = \sqrt[5]{2^6}`=

`2^ (6)/(5)=(2^ (5)/(5))(2^ (1)/(5))=2 \sqrt[5]{2}`

also, 4^3=64


so possible ones are

`2^ (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}`)