Question

Which of the following questions are equivalent to the answer below x 3/5

Answer 1

`x^(3)/(5) = (x^3 )^(1)/(5)`

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

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

Explanation:

Given

`x^(3)/(5)`

Required

The equivalent expressions

We have:

`x^(3)/(5)`

Expand the exponent

`x^(3)/(5) = x^{ 3 * (1)/(5)}`

So, we have:

`x^(3)/(5) = (x^3 )^(1)/(5)` ----- this is equivalent

Express 1/5 as roots (law of indices)

`x^(3)/(5) = \sqrt[5]{x^3}` ------ this is equivalent

The above can be rewritten as:

`x^(3)/(5) = (\sqrt[5]{x})^3` ------ this is equivalent