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. 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

Question

Use the law of exponents to find the power with the algebraic fraction below.
x over y squared

Step-by-Step:

1

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

2

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

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

4

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

Answer:

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 (a⁄b)n.
  • The base is the algebraic fraction a⁄b.
  • 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

Lesson Slides

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

What Is an Algebraic Fraction?

An algebraic fraction is a fraction which contains letters.