Simplify the Exponent Division: 2^4 ÷ 2^3

Question

2423= \frac{2^4}{2^3}=

Video Solution

Solution Steps

00:06 Let's get started!
00:09 We're going to use a formula for dividing with exponents.
00:13 When we divide A to the power of M by A to the power of N.
00:17 It's equal to A raised to the power of M minus N.
00:21 Let's try this formula in our exercise.
00:25 Keep the base A, then subtract the exponents M minus N.
00:30 Remember, A to the power of 1 is just A.
00:34 And that's how we solve this problem!

Step-by-Step Solution

Let's keep in mind that the numerator and denominator of the fraction have terms with the same base, therefore we use the property of powers to divide between terms with the same base:

bmbn=bmn \frac{b^m}{b^n}=b^{m-n}

We apply it in the problem:

2423=243=21 \frac{2^4}{2^3}=2^{4-3}=2^1

Remember that any number raised to the 1st power is equal to the number itself, meaning that:

b1=b b^1=b

Therefore, in the problem we obtain:

21=2 2^1=2

Therefore, the correct answer is option a.

Answer

2 2