How to cube a fraction?
Understand the Problem
The question is asking how to perform the mathematical operation of cubing a fraction. Cubing a fraction involves raising both the numerator and the denominator to the power of three.
Answer
The cube of the fraction $\frac{a}{b}$ is $\frac{a^3}{b^3}$.
Answer for screen readers
The result of cubing the fraction $\frac{a}{b}$ is $\frac{a^3}{b^3}$.
Steps to Solve
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Identify the fraction Start with the fraction you want to cube. Let's say the fraction is $\frac{a}{b}$.
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Cube the numerator Raise the numerator to the power of three: $$ a^3 $$
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Cube the denominator Raise the denominator to the power of three: $$ b^3 $$
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Combine the results Put the cubed numerator and cubed denominator together: $$ \left(\frac{a}{b}\right)^3 = \frac{a^3}{b^3} $$
The result of cubing the fraction $\frac{a}{b}$ is $\frac{a^3}{b^3}$.
More Information
Cubing a fraction is simply an application of the power rule for fractions. This rule states that when you raise a fraction to a power, you can raise both the numerator and the denominator to that power independently. This process is the same regardless of the specific values of $a$ and $b$.
Tips
- Not cubing both parts: Sometimes, people forget to cube both the numerator and the denominator which leads to incorrect results. Always remember to apply the operation to both parts of the fraction.
