Question

simplify. express your answer using positive exponents
$a^3 \cdot a^9$

Explanation:

Step1: Recall exponent rule for multiplication

When multiplying two powers with the same base, we add the exponents: \(a^m \cdot a^n = a^{m + n}\).

Step2: Apply the rule to \(a^3 \cdot a^9\)

Here, \(m = 3\) and \(n = 9\), so we add the exponents: \(3 + 9 = 12\). Thus, \(a^3 \cdot a^9 = a^{3 + 9}=a^{12}\).

Answer:

\(a^{12}\)