Simplify the Expression: 9^(2a) × 9^(2x) × 9^a with Multiple Exponents

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

• Step 1: Recognize that all the terms have the same base, which is 9.
• Step 2: Apply the exponent addition rule to combine the exponents.
• Step 3: Simplify the result by performing algebraic addition on the exponents.

Now, let's work through each step:
Step 1: The problem gives us the expression $9^{2a} \times 9^{2x} \times 9^a$. All terms share the same base, which is 9.
Step 2: Using the property of exponents $b^m \times b^n = b^{m+n}$, add the exponents: $(2a) + (2x) + a$.
Step 3: Combine like terms: $2a + a + 2x = 3a + 2x$. So, the expression becomes $9^{3a+2x}$.

Therefore, the simplified form of the given equation is $9^{3a+2x}$.