Simplify the Expression: 2² × 2³ Using Laws of Exponents

Question

Simplify the following equation:

22×23= 2^2\times2^3=

Video Solution

Solution Steps

00:00 Simplify the following problem
00:03 According to the laws of exponents, the multiplication of exponents with an equal base (A)
00:07 is equal to the same base raised to the sum of the exponents (N+M)
00:11 We will apply this formula to our exercise
00:14 We will add up the exponents and raise them to this power
00:17 This is 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}