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How to Find a Power of an Algebraic Fraction (Mathematics Lesson)

Finding a Power of an Algebraic Fraction

A power can have an algebraic fraction raised to an exponent.

Imagine we have an algebraic fraction ab with an exponent n. We raise both top and bottom of the fraction to the exponent n. This is equal to anbn.

The power of an algebraic fraction is equal to the numerator and the denominator both raised to the power

This is a laws of exponents.

How to Find a Power of an Algebraic Fraction

An Example Question

Use the law of exponents to find the power with the algebraic fraction below.

x over y squared
Step 1

Find the exponent of the power. In our example, the exponent is 2.

Step 2

Find the top letter (called the numerator) of the fraction. In our example, the numerator is x.

The numerator is x
Step 3

Raise the letter found in Step 2 (x) to the exponent found in Step 1 (2). This becomes the numerator of the answer.

The numerator of the answer is x squared
Step 4

Find the bottom letter (called the denominator) of the fraction. In our example, the denominator is y.

The denominator is y
Step 5

Raise the letter found in Step 4 (y) to the exponent found in Step 1 (2). This becomes the denominator of the answer.

The denominator of the answer is y squared

We have found the power of an algebraic fraction.

x squared over y squared

Understanding Finding a Power of an Algebraic Fraction

Let us look at the rule for powers of an algebraic fraction:

bases and exponents

Firstly, let us look at what is to the left of the equals sign (=):

  • The power is (ab)n.

  • The base is the algebraic fraction ab.

  • The exponent is n.

Let us look at the right hand side of the equals sign (=):

  • The right hand side is an algebraic fraction.

  • The top of the fraction is a power: an. It has a base of a with an exponent of n.

  • The bottom of the fraction is a power: bn. It has a base of b with an exponent of n.

More Examples of Finding the Power of an Algebraic Fraction

Algebraic fractions do not just contain single letters.

  • When an algebraic fraction has a number, we can find the power:

    The power of x over 2 is x squared over 2 squared
  • When an algebraic fraction has a term, we can find the power. Notice that the whole term is raised to the exponent:

    The power of 2 x over y is 2 x squared over y squared
  • When an algebraic fraction has a expression, we can find the power. Notice that the whole expression is raised to the exponent:

    The power of x plus y over z is x plus y all squared over z squared

Another Real Example of How to Find the Power of an Algebraic Fraction

The slider below shows another real example of how to find the power of an algebraic fraction.

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Here's a second test on finding powers of an algebraic fraction.
Here's a third test on finding powers of an algebraic fraction.

Note

What Is an Algebraic Fraction?

An algebraic fraction is a fraction which contains letters.