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

Solution:

Given, the fourth root of 7 to the fifth power.

We have to write the radical as a rational exponent.

The formula to change a radical to rational exponent is given by

\(\sqrt[n]{a^{m}}=a^{\frac{m}{n}}\)

Now, cube root of 2 to the seventh power can be written as \(\sqrt[3]{2^{7}}\)

So, \(\sqrt[4]{7^{5}}=7^{\frac{5}{4}}\)

Therefore, the rational exponent is \(7^{\frac{5}{4}}\).

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

Summary:

The radical fourth root of 7 to the fifth power as a rational exponent \(7^{\frac{5}{4}}\).