Solve the Cube Expression: Simplifying 1/8³ Step by Step

183=? \frac{1}{8^3}=\text{?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:03 Let's learn how to switch a fraction with a positive exponent into one with a negative exponent.
00:09 When a number A is raised to the power of negative N, it's equal to one divided by A raised to the power of N.
00:16 So, if we use this rule, we can change numbers between fractions and whole numbers easily.
00:22 For example, one divided by eight becomes eight.
00:26 And the power of three changes to negative three.
00:30 And that's the solution!

Step-by-step written solution

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1

Understand the problem

183=? \frac{1}{8^3}=\text{?}

2

Step-by-step solution

We use the negative exponent rule.

b−n=1bn b^{-n}=\frac{1}{b^n}

We apply it to the problem in the opposite sense.:

183=8−3 \frac{1}{8^3}=8^{-3}

Therefore, the correct answer is option A.

3

Final Answer

8−3 8^{-3}

Practice Quiz

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

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