Question

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

Explanation:

Step1: Apply negative exponent rule

A negative exponent means the 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:

$-\frac{1}{8}$