Question

fill in the blank 1 point
$16^3 \cdot (-7)^{-3} = $ answer
options (from left to right, top to bottom):
$5^9/(11^7 \cdot 6^9)$
$(3^5 \cdot 7^7)/(-21)^4$
$16^3/(-7)^3$
$6^9/(11^7 \cdot 5^9)$
$(7^5 \cdot (-4)^7)/(3^5 \cdot (-21)^4)$
$1/(8 \cdot 21)^4$
$16^3 / 7^3$
$7^9 / 16^9$
$(3^5 \cdot 21^4)/(7^9 \cdot (-4)^{10})$
$8 / 21^3$
$(6^9 \cdot 5^9)/11^7$
$21^{14} / 8^6$
$16^3/(-7)^3$ (duplicate option)

Explanation:

Step1: Rewrite negative exponent

Recall $a^{-n}=\frac{1}{a^n}$, so $(-7)^{-3}=\frac{1}{(-7)^3}$.
Expression: $16^3 \cdot \frac{1}{(-7)^3}$

Step2: Combine into single fraction

Multiply the terms to get a single rational expression.
Expression: $\frac{16^3}{(-7)^3}$

Answer:

$\frac{16^3}{(-7)^3}$