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

Question

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

Video Solution

Solution Steps

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 Solution

We use the negative exponent rule.

$b^{-n}=\frac{1}{b^n}$

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

$\frac{1}{8^3}=8^{-3}$

Therefore, the correct answer is option A.

Answer

$8^{-3}$

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Question Types

Negative Exponents: Calculating powers with negative exponents Negative Exponents: Presenting powers in the denominator as powers with negative exponents Negative Exponents: Presenting powers with negative exponents as fractions Applying Combined Exponents Rules: Calculating powers with negative exponents Applying Combined Exponents Rules: Presenting powers in the denominator as powers with negative exponents Applying Combined Exponents Rules: Presenting powers with negative exponents as fractions Applying Combined Exponents Rules: Monomial