Question

What is this expression in rational exponent form cuberoot√5xy^2

Answer 1

`5^{(1)/(3)}x^{(1)/(3)}y^{(2)/(3)}`.

Explanation:

The given expression is

`\sqrt[3]{5xy^2}`

We need to find the expression in rational exponent form.

It can be written as

`(5xy^2)^{(1)/(3)}`
`[\because \sqrt[n]{x}=x^{(1)/(n)}]`

`=(5)^{(1)/(3)}(x)^{(1)/(3)}(y^2)^{(1)/(3)}`
`[\because (ab)^m=a^mb^m]`

`=5^{(1)/(3)}x^{(1)/(3)}y^{(2)/(3)}`
`[\because (a^m)^n=a^(mn)]`

Therefore, the required expression is
`5^{(1)/(3)}x^{(1)/(3)}y^{(2)/(3)}`.