Simplify the Expression: 3² × 3³ Using Laws of Exponents

Question

Simplify the following equation:

32×33= 3^2\times3^3=

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)
00:13 We will apply this formula to our exercise
00:17 We will then proceed to add up the exponents and raise them to this power
00:20 This is the solution

Step-by-Step Solution

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

  • Step 1: Identify the base and exponents
  • Step 2: Apply the exponent multiplication rule
  • Step 3: Perform the calculations

Let's work through each step:
Step 1: We have 32 3^2 and 33 3^3 . Both have the same base, which is 3.
Step 2: According to the exponent multiplication rule am×an=am+n a^m \times a^n = a^{m+n} , we add the exponents:
2+3=5 2 + 3 = 5 .
Step 3: Rewrite the expression as a single power:
32×33=32+3=35 3^2 \times 3^3 = 3^{2+3} = 3^5 .

Therefore, the simplified expression is 35\boldsymbol{3^5}, which corresponds to choice 2.

Answer

35 3^5