Simplify the Expression: 9^-3 × 9^-5 × 9^-2 Using Exponent Laws

To solve this problem, we'll follow these steps:

• Step 1: Identify the common base.
• Step 2: Apply the multiplication of powers rule.
• Step 3: Simplify by adding the exponents.

Now, let's work through each step:
Step 1: The base in every term of the expression $9^{-3} \times 9^{-5} \times 9^{-2}$ is 9.
Step 2: Use the exponent multiplication rule $a^m \times a^n = a^{m+n}$.
Step 3: Add the exponents: $-3 + (-5) + (-2) = -10$.
The expression simplifies to $9^{-10}$.

Therefore, the solution to the problem is $9^{-10}$.