Fraction Power Calculator

Enter a fraction, select the power, and quickly calculate the result.

Fraction Power Calculate

Fraction
Result

What Is a Power?

In mathematics, a power represents the repeated multiplication of a number by itself. It is usually written as \( a^n \), where \( a \) is the base, and \( n \) is the exponent. Powers can be applied to integers, fractions, and mixed numbers.

How to Calculate the Power of a Fraction?

Given a fraction and an exponent, the steps to calculate the power are as follows:

  1. Identify the Fraction and Power: Let the fraction be \( \frac{a}{b} \) (which can be a regular fraction or a mixed number), and the power be \( n \).
  2. Convert Mixed Numbers to Improper Fractions (if applicable): If the input is a mixed number, first convert it to an improper fraction. For example, \( 1 \frac{1}{2} = \frac{3}{2} \).
  3. Apply the Power Formula: \( x = \left(\frac{a}{b}\right)^n = \frac{a^n}{b^n} \)

Examples

Example 1: Calculate the square of \(\frac{3}{4}\).

Solution:

Compute:

\( x = \left(\frac{3}{4}\right)^2 = \frac{3^2}{4^2} = \frac{9}{16}\)

Conclusion: The square of \(\frac{3}{4}\) is \(\frac{9}{16}\).

Example 2: Calculate the cube of \( \frac{2}{5} \).

Solution:

Compute:

\( x = \left(\frac{2}{5}\right)^3 = \frac{2^3}{5^3} = \frac{8}{125}\)

Thus, the cube of \( \frac{2}{5} \) is \(\frac{8}{125}\).

Example 3: Calculate the square of \( 1 \frac{1}{4} \) (i.e., \( \frac{5}{4} \)).

Solution:

Convert to an improper fraction:

\( 1 \frac{1}{4} = \frac{5}{4}\)

Compute:

\( x = \left(\frac{5}{4}\right)^2 = \frac{5^2}{4^2} = \frac{25}{16}\)

Result: the square of \( 1 \frac{1}{4} \) is \(\frac{25}{16}\).