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

9⋅380=? \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

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1

Understand the problem

9⋅380=? \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

Practice Quiz

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

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