Simplify cube root of 7 / Fifth root of 7

A. 7 to the power of 1 over 5
B. 7 to the power of 8 over 15
C. 7 to the power of 5 over 3
D. 7 to the power of 2 over 15

Respuesta :

7^(1/3) : 7^( 1/5)= 7^(1/3 -1/5)=7^[(5-3)/15]= 7^[2/15]

the answer is D

Answer:

Option D. is the answer.

Step-by-step explanation:

we have to simplify the cube root of [tex]\frac{\sqrt[3]{7}}{\sqrt[5]{7} }[/tex]

= [tex]\frac{7^{\frac{1}{3}}}{7^{\frac{1}{5} } }[/tex]

= [tex]7^{\frac{1}{3}-\frac{1}{5}}[/tex]

= [tex]7^{(\frac{5-3}{15})}[/tex]

= [tex]7^{\frac{2}{15}}[/tex]

Therefore, Option D. 7 to the power of 2 over 15 is the answer.