Question

evaluate. write your answer as a whole number or as a simplified fraction. 9^{-2} cdot 2^{-3} = \frac{\quad}{\quad}

Explanation:

Step1: Rewrite negative exponents

Recall $a^{-n}=\frac{1}{a^n}$.
$9^{-2}=\frac{1}{9^2}$, $2^{-3}=\frac{1}{2^3}$

Step2: Calculate positive powers

$9^2=81$, $2^3=8$

Step3: Multiply the fractions

$\frac{1}{81} \cdot \frac{1}{8} = \frac{1}{81 \times 8}$

Step4: Compute denominator product

$81 \times 8 = 648$

Answer:

$\frac{1}{648}$