Simplify the Expression: 9² × 9⁹ Using Exponent Properties

Simplify the following equation:

$9^2\times9^9=$

Video Solution

Solution Steps

00:00 Simplify the following problem

00:03 According to the laws of exponents, the multiplication of exponents with an equal base (A)

00:07 equals the same base raised to the sum of the exponents (N+M)

00:12 We will apply this formula to our exercise

00:15 We will then add up the exponents and raise them to this power

00:22 This is the solution

Step-by-Step Solution

To solve this problem, we'll simplify the expression $9^2 \times 9^9$ using the multiplication of powers rule:

Step 1: Identify the base and the exponents. The base here is 9, and the exponents are 2 and 9.
Step 2: Apply the rule for multiplying powers with the same base: $a^m \times a^n = a^{m+n}$ .
Step 3: Add the exponents: $9^2 \times 9^9 = 9^{2+9} = 9^{11}$ .

The expression simplifies to $9^{11}$ .

Therefore, the simplified expression is $9^{11}$ , which matches choice 1.