The Lesson
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
Question
Use the law of exponents to find the power with the algebraic fraction below.StepbyStep:
1
Find the exponent of the power. In our example, the exponent is 2.
2
3
Raise the letter found in Step 2 (x) to the exponent found in Step 1 (2). This becomes the numerator of the answer.
4
Find the bottom letter (called the denominator) of the fraction. In our example, the denominator is y.
5
Raise the letter found in Step 4 (y) to the exponent found in Step 1 (2). This becomes the denominator of the answer.
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: