Question

Which of the following best explains how to find the value of
8
5
3
?


A number with an exponent of
5
3
is the same as 5 times the cube root of the number.


A number with an exponent of
5
3
is the same as the cube root of the number raised to the 5th power.


Each time
8
x
doubles, the exponent is multiplied by
1
3
.


Each time x increases by
1
3
, the value of
8
x
is multiplied by 8.

Answer 1

The second choice. For any positive a, a^(5/3) = (a^(1/3))^5 (equivalently = (a^5)^(1/3)). So 8^(5/3) = (cube root of 8)^5 = 2^5 = 32.