(1/2)^-3 I know the answer is 8, but how?

Question

how do you multiply a fraction by a negative exponent?

Answer 1

((1)/(2))^(-3)

Expand the exponent (3) to the expression.
(1)/((1)/((2)^(3)))

Expand the exponent (3) to the expression.
(1)/((1)/(2^(3)))

Cubing a number is the same as multiplying the number by itself 3 times (2*2*2).  In this case, 2 cubed is 8.
(1)/((1)/(8))

To divide by (1)/(8), multiply by the reciprocal of the fraction.
8