Simplify the Expression: 2² × 2³ Using Laws of Exponents

Question

Simplify the following equation:

22×23= 2^2\times2^3=

Video Solution

Solution Steps

00:06 Let's simplify this problem together.
00:09 When multiplying numbers with the same base, like A,
00:13 you add the exponents, so it becomes A to the power of N plus M.
00:18 Now, we will use this rule in our example.
00:21 Add the exponents and apply this new power.
00:25 That's how we find the solution!

Step-by-Step Solution

To simplify the expression 22×23 2^2 \times 2^3 , we apply the rule for multiplying powers with the same base. According to this rule, when multiplying two exponential expressions that have the same base, we keep the base and add the exponents.

  • Step 1: Identify the base: In this problem, the base for both terms is 2.
  • Step 2: Apply the exponent multiplication rule: 22×23=22+3 2^2 \times 2^3 = 2^{2+3} .
  • Step 3: Simplify by adding the exponents: 22+3=25 2^{2+3} = 2^5 .

Thus, the simplified form of the expression 22×23 2^2 \times 2^3 is 25 2^{5} .

The correct choice from the provided options is: 22+3 2^{2+3} .

Answer

22+3 2^{2+3}