Question

Please help!
Rewrite the rational exponent as a radical. (2 points)

Answer 1

Answer: 3)
`√(5)`

Explanation:

Radical Form and Exponent Form

A radical can be expressed as a rational exponent following the identity:

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

We should also recall that:

`(x^n)^m=x^(nm)`

We are given the expression:

`\displaystyle \left(5^{(3)/(4)}\right)^(2)/(3)`

Applying the power of power:

`\displaystyle \left(5^{(3)/(4)}\right)^(2)/(3)=\left(5^{(3)/(4)\cdot (2)/(3)}\right)`

Simplifying:

`\displaystyle \left(5^{(3)/(4)}\right)^(2)/(3)=5^{(1)/(2)}`

Converting to radical form:

`\displaystyle \left(5^{(3)/(4)}\right)^(2)/(3)=√(5)`

Answer: 3)
`√(5)`