Question

Simplify cube root of 7 over fifth root of 7. 7 to the power of one fifth 7 to the power of eight fifteenths 7 to the power of five thirds 7 to the power of two fifteenths

Answer 1

D. 7 to the power of two fifteenths

Explanation:

Answer 2

`\huge\boxed{7^{(2)/(15)}}`

Explanation:

`(\sqrt[3]7)/(\sqrt[5]7)\qquad\text{use}\ a^(1)/(n)=\sqrt[n]{a}\\\\=(7^(1)/(3))/(7^(1)/(5))\qquad\text{use}\ (a^n)/(a^m)=a^(n-m)\\\\=7^{(1)/(3)-(1)/(5)}\qquad\text{find the common denominator (15)}\\\\=7^{((1)(5))/((3)(5))-((1)(3))/((5)(3))}=7^{(5-3)/(15)}=7^{(2)/(15)}`