Solve (9·3)÷8^0: Zero Exponent Division Problem

Zero Exponent Rule with Multiplication

9380=? \frac{9\cdot3}{8^0}=\text{?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Simplify the following problem
00:03 According to the power laws, a number raised to the power 0 equals 1
00:06 As long as the number is not 0
00:09 We will apply this formula to our exercise
00:14 A number divided by 1 is the number itself
00:20 We'll break down 9 into 3 squared
00:24 When multiplying powers with equal bases
00:27 The power of the result equals the sum of the powers
00:33 We'll apply this formula to our exercise, we'll then proceed to add up the powers
00:37 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

9380=? \frac{9\cdot3}{8^0}=\text{?}

2

Step-by-step solution

We use the formula:

a0=1 a^0=1

9×380=9×31=9×3 \frac{9\times3}{8^0}=\frac{9\times3}{1}=9\times3

We know that:

9=32 9=3^2

Therefore, we obtain:

32×3=32×31 3^2\times3=3^2\times3^1

We use the formula:

am×an=am+n a^m\times a^n=a^{m+n}

32×31=32+1=33 3^2\times3^1=3^{2+1}=3^3

3

Final Answer

33 3^3

Key Points to Remember

Essential concepts to master this topic
  • Zero Exponent Rule: Any non-zero number raised to power 0 equals 1
  • Technique: Replace 80 8^0 with 1, then calculate 9×3=27 9 \times 3 = 27
  • Check: Verify 27=33 27 = 3^3 since 3×3×3=27 3 \times 3 \times 3 = 27

Common Mistakes

Avoid these frequent errors
  • Thinking zero exponent equals zero
    Don't assume 80=0 8^0 = 0 = undefined division! This makes students think the answer is undefined or zero. Always remember: any non-zero base to the power of 0 equals 1, so 80=1 8^0 = 1 .

Practice Quiz

Test your knowledge with interactive questions

Which of the following is equivalent to \( 100^0 \)?

FAQ

Everything you need to know about this question

Why does any number to the power of 0 equal 1?

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Think of it as the pattern rule! When you divide powers: 83÷83=833=80 8^3 \div 8^3 = 8^{3-3} = 8^0 . Since any number divided by itself equals 1, we get 80=1 8^0 = 1 !

What if the base is 0? Does 00 0^0 equal 1?

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00 0^0 is actually undefined in mathematics! The zero exponent rule only works for non-zero bases. So 80=1 8^0 = 1 , but 00 0^0 is undefined.

How do I simplify 9×3 9 \times 3 to get 33 3^3 ?

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First calculate: 9×3=27 9 \times 3 = 27 . Then recognize that 9=32 9 = 3^2 , so 32×31=32+1=33 3^2 \times 3^1 = 3^{2+1} = 3^3 . Finally check: 33=3×3×3=27 3^3 = 3 \times 3 \times 3 = 27

Why can't I just cancel the 8 in numerator and denominator?

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There's no 8 in the numerator to cancel! We have 9×380 \frac{9 \times 3}{8^0} , not 8×380 \frac{8 \times 3}{8^0} . Only identical factors can be cancelled.

Do I need to convert everything to the same base?

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Not necessary for this problem! You can solve it step-by-step: 80=1 8^0 = 1 , then 9×3=27 9 \times 3 = 27 . Converting to 33 3^3 is just the final step to match the answer choices.

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