Question

rewrite each expression using only positive exponents. the answers are mixed up at the bottom of each problem.
1 fill in the blank 1 point
$7^3 \cdot 16^{-9} = $
answer
$6^9/(11^7 \cdot 5^9)$
$1/(8 \cdot 21)^4$
$(6^9 \cdot 5^9)/11^7$
$(7^5 \cdot (-4)^2)/(3^5 \cdot (-21)^4)$
$21^4/8^6$
$8/21^3$
$7^3/16^9$
$16^3/7^3$
$(3^5 \cdot 21^4)/(7^9 \cdot (-4)^{10})$
$5^9/(11^7 \cdot 6^9)$
$(3^5 \cdot 7^7)/(-21)^4$
$16^3/(-7)^3$
$7^3/16^9$

Explanation:

Step1: Apply negative exponent rule

Recall that $a^{-n} = \frac{1}{a^n}$, so rewrite $16^{-9}$:
$7^3 \cdot 16^{-9} = 7^3 \cdot \frac{1}{16^9}$

Step2: Combine into single fraction

Multiply the terms to form one fraction:
$\frac{7^3}{16^9}$

Answer:

$\frac{7^3}{16^9}$