Question

rewrite the following without an exponent.
$(-2)^{-3}$

Explanation:

Step1: Apply negative exponent rule

A negative exponent means reciprocal: $a^{-n} = \frac{1}{a^n}$, so
$(-2)^{-3} = \frac{1}{(-2)^3}$

Step2: Calculate the denominator

Compute the positive exponent:
$(-2)^3 = (-2) \times (-2) \times (-2) = -8$

Step3: Simplify the fraction

Substitute the denominator value:
$\frac{1}{(-2)^3} = \frac{1}{-8} = -\frac{1}{8}$

Answer:

$-\frac{1}{8}$