Question

Simplify cube root of 7 over fifth root of 7. (5 points)

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

Answer 1

The numerator of our fraction is the "cube root of 7" which can be expressed as 7^(1/3). In the same manner, our denominator is "fifth root of 7" which is equal to 7^(1/5).

The mathematical expression of the given is,

s = 7^(1/3) / 7^(1/5)

Since the numbers have the same bases, it can also become,
s = 7^(1/3 - 1/5)

The simplification of the operation above is,
s = 7^(2/15)

Hence, the answer to this item is letter D.