Simplify the Expression: 9² × 9⁹ Using Exponent Properties

Simplify the following equation:

92×99= 9^2\times9^9=

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Step-by-step video solution

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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 written solution

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1

Understand the problem

Simplify the following equation:

92×99= 9^2\times9^9=

2

Step-by-step solution

To solve this problem, we'll simplify the expression 92×99 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: am×an=am+n a^m \times a^n = a^{m+n} .
  • Step 3: Add the exponents: 92×99=92+9=911 9^2 \times 9^9 = 9^{2+9} = 9^{11} .

The expression simplifies to 911 9^{11} .

Therefore, the simplified expression is 911 9^{11} , which matches choice 1.

3

Final Answer

911 9^{11}

Practice Quiz

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Simplify the following equation:

\( 2^2\times2^3= \)

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