Simplify the Product: 2¹ × 2² × 2³ Using Exponent Rules

Question

Simplify the following equation:

21×22×23= 2^1\times2^2\times2^3=

Video Solution

Solution Steps

00:00 Simplify the following problem
00:03 According to the laws of exponents, the multiplication of powers with an equal base (A)
00:08 equals the same base raised to the sum of the exponents (N+M)
00:12 We will apply this formula to our exercise
00:17 We'll maintain the base and add together the exponents
00:29 This is the solution

Step-by-Step Solution

To simplify the expression 21×22×232^1 \times 2^2 \times 2^3, we'll apply the rule for multiplying powers with the same base:

  • When multiplying powers with the same base, you add the exponents.

Let's apply this to our expression:

21×22×23=21+2+32^1 \times 2^2 \times 2^3 = 2^{1+2+3}

Now, calculate the sum of the exponents: 1+2+3=61 + 2 + 3 = 6.

Thus, the expression simplifies to

262^6.

By comparing it with the given choices, the correct simplified form, 21+2+32^{1+2+3}, corresponds to choice 2:
21+2+32^{1+2+3}.

Answer

21+2+3 2^{1+2+3}