Question

Rewrite the radical as a rational exponent. the fourth root of 7 to the fifth power

Answer 1

7^5/4 would be the answer to the question I think you are asking

Answer 2

`\sqrt[4]{7^5}=7^{(5)/(4)}`

Explanation:

Given: "the fourth root of 7 to the fifth power"

First we write as radical form and then convert into rational fraction as per rule of exponent.

`\text{the fourth root of 7 to the fifth power}=\sqrt[4]{7^5}`

`\sqrt[n]{x^m}`

• m, Power goes at numerator of rational exponent.

• n , nth root goes at denominator of rational exponent.

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

In the given radical,
`\sqrt[4]{7^5}`

m=5 and n=4

now, we write radical as a rational exponent.

`\sqrt[4]{7^5}=7^{(5)/(4)}`