How to Find a Power of a Fraction (Mathematics Lesson)
Finding a Power of a Fraction
A power can have an fraction raised to an exponent.
Imagine we have a fraction ^{2}⁄_{3} with an exponent n. We raise both top and bottom of the fraction to the exponent n. This is equal to ^{2n}⁄_{3n}.
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 fraction below.
Find the exponent of the power. In our example, the exponent is 2.
Find the top number (called the numerator) of the fraction. In our example, the numerator is 3.
Raise the number found in Step 2 (3) to the exponent found in Step 1 (2). This becomes the numerator of the answer.
Find the bottom number (called the denominator) of the fraction. In our example, the denominator is 4.
Raise the number found in Step 4 (4) to the exponent found in Step 1 (2). This becomes the denominator of the answer.
We have used the law of exponents to find the power of a fraction.
For the final steps, evaluate the powers in our fraction.
Evaluate the power on the top of the fraction. In our example, evaluate 3^{2}.
Evaluate the power on the bottom of the fraction. In our example, evaluate 4^{2}.
(^{3}⁄_{4})^{2} is equal to ^{9}⁄_{16}.
Understanding Finding a Power of a Fraction
Let us look at the rule for powers of a 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 a fraction.

The top of the fraction is a power: 2^{n}. It has a base of 2 with an exponent of n.

The bottom of the fraction is a power: 3^{n}. It has a base of 3 with an exponent of n.
Another Real Example of How to Find the Power of a Fraction
The slider below shows another real example of how to find the power of a fraction.