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Finding a Power of an Algebraic Fraction

(KS3, Year 8)

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.

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.

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. 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:
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: