Question

Simplify 64^-1/3
A. -4
B. -1/4
C. 1/4
D. 4

Answer 1

The answer is C. 1/4

Since the exponent is a negative it wouldn't be 4 it would turn into 1/4

Answer 2

Remember, the numerator of an exponenent represents the root. As well, a negative exponent means to take the reciprocal of the positive exponent (
`a^(-b) = (1)/(a^(b))`.

So,
`64^(-1/3)` is equal to
`\sqrt[3]{64^(-1)}` which is 1/4, because 1/4*1/4*1/4 is 1/64 (1/64 cubed root is 1/4).

For example,
`a^(b/c) = \sqrt[c]{b^(b)}`

The answer is c.