Answer:
[tex]\sqrt[4]{7^5}=7^{\frac{5}{4}}[/tex]
Step-by-step 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.
[tex]\text{the fourth root of 7 to the fifth power}=\sqrt[4]{7^5}[/tex]
[tex]\sqrt[n]{x^m}[/tex]
So, [tex]\sqrt[n]{x^m}=x^{\frac{m}{n}}[/tex]
In the given radical, [tex]\sqrt[4]{7^5}[/tex]
m=5 and n=4
now, we write radical as a rational exponent.
[tex]\sqrt[4]{7^5}=7^{\frac{5}{4}}[/tex]
