Simplify the expression $a^3 \times (-3a)^2$.

1. Problem Description

Simplify the expression $a^3 \times (-3a)^2$.

2. Solution Steps

First, we simplify the term $(-3a)^2$:

$(-3a)^2 = (-3)^2 \times a^2 = 9a^2$

Now we substitute this back into the original expression:

$a^3 \times (-3a)^2 = a^3 \times 9a^2$

Using the exponent rule $a^m \times a^n = a^{m+n}$:

$a^3 \times 9a^2 = 9 \times a^3 \times a^2 = 9a^{3+2} = 9a^5$

3. Final Answer

$9a^5$