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 ^{a}⁄_{b} with an exponent n. We raise both top and bottom of the fraction to the exponent n. This is equal to ^{an}⁄_{bn}.
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.
Find the exponent of the power. In our example, the exponent is 2.
Find the top letter (called the numerator) of the fraction. In our example, the numerator is x.
Raise the letter found in Step 2 (x) to the exponent found in Step 1 (2). This becomes the numerator of the answer.
Find the bottom letter (called the denominator) of the fraction. In our example, the denominator is y.
Raise the letter found in Step 4 (y) to the exponent found in Step 1 (2). This becomes the denominator of the answer.
We have found the power of an algebraic fraction.
Understanding Finding a Power of an Algebraic Fraction
Let us look at the rule for powers of an algebraic fraction:
Firstly, let us look at what is to the left of the equals sign (=):
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: a^{n}. It has a base of a with an exponent of n.

The bottom of the fraction is a power: b^{n}. 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:

When an algebraic fraction has a term, we can find the power. Notice that the whole term is raised to the exponent:

When an algebraic fraction has a expression, we can find the power. Notice that the whole expression is raised to the exponent:
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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Interactive Test
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