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

Exponent Division with Same Base

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
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 written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

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

2

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.

3

Final Answer

2 2

Key Points to Remember

Essential concepts to master this topic
  • Rule: When dividing powers with same base, subtract exponents
  • Technique: 2423=243=21 \frac{2^4}{2^3} = 2^{4-3} = 2^1
  • Check: Verify by expanding: 168=2 \frac{16}{8} = 2

Common Mistakes

Avoid these frequent errors
  • Adding exponents instead of subtracting
    Don't add the exponents (4 + 3 = 7) to get 27=128 2^7 = 128 ! This gives a massive wrong answer because you're using the multiplication rule instead. Always subtract exponents when dividing: bmbn=bmn \frac{b^m}{b^n} = b^{m-n} .

Practice Quiz

Test your knowledge with interactive questions

\( 112^0=\text{?} \)

FAQ

Everything you need to know about this question

Why do we subtract exponents when dividing?

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Because division undoes multiplication! When you multiply 23×21 2^3 \times 2^1 , you add exponents to get 24 2^4 . So dividing reverses this by subtracting.

What happens when I get an exponent of 1?

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Any number to the first power equals itself! So 21=2 2^1 = 2 , 51=5 5^1 = 5 , etc. This is why our final answer is just 2.

Can I just calculate the powers first then divide?

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Yes, but it's harder! You'd need to calculate 24=16 2^4 = 16 and 23=8 2^3 = 8 , then divide 16 ÷ 8 = 2. The exponent rule is much faster!

What if the exponents were the same?

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If you had 2424 \frac{2^4}{2^4} , you'd get 244=20=1 2^{4-4} = 2^0 = 1 . Any non-zero number divided by itself equals 1!

Does this work with different bases?

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No! This rule only works when the bases are the same. For 2433 \frac{2^4}{3^3} , you must calculate each power separately, then divide.

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