Question

Rewrite the expression with a rational exponent as a radical expression.

Answer 1

Rewriting the expression
`(3^(2)/(3))^(1)/(6)` with a rational exponent as a radical expression we get
`\mathbf{\sqrt[9]{3} }`

Explanation:

We need to rewrite the expression
`(3^(2)/(3))^(1)/(6)` with a rational exponent as a radical expression.

The expression given is:

`(3^(2)/(3))^(1)/(6)`

First we will simply the expression using exponent rule
`(a^m)^n=a^(mn)`

`(3^(2)/(3))^(1)/(6)\\=(3^(2)/(18))`

As we know 2 and 18 are both divisible by 2, we can write

`=(3^(1)/(9))`

Now we know that
`a^(1)/(9)=\sqrt[9]{a}`

Using this we get

`=\sqrt[9]{3}`

So, rewriting the expression
`(3^(2)/(3))^(1)/(6)` with a rational exponent as a radical expression we get
`\mathbf{\sqrt[9]{3} }`