Question

12
(a) which rule of exponents would you use to simplify the expression $9^3 \times 9^7$ ?
a quotient rule
b power rule
c zero power rule
d product rule
e negative exponent rule
(b) what is the simplified expression after applying this rule?
$square$

Explanation:

Step1: Identify the exponent rule

The expression is $9^3 \times 9^7$, which multiplies two terms with the same base. This matches the Product Rule, which states $a^m \times a^n = a^{m+n}$.

Step2: Apply the Product Rule

Substitute $a=9$, $m=3$, $n=7$ into the rule:
$9^{3+7} = 9^{10}$

Answer:

(a) D. Product Rule
(b) $9^{10}$