Question

rewrite using a single positive exponent.
$7^{9} \cdot 7^{-3}$

Explanation:

Step1: Recall exponent rule for multiplication

When multiplying two powers with the same base, we add the exponents: $a^m \cdot a^n = a^{m + n}$. Here, the base $a = 7$, $m = 9$, and $n=-3$.
$$7^9 \cdot 7^{-3}=7^{9+(-3)}$$

Step2: Simplify the exponent

Calculate $9 + (-3)$ which is $9 - 3 = 6$.
$$7^{9+(-3)} = 7^6$$

Answer:

$7^6$