The Lesson
A power can have an fraction raised to an exponent. 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 fraction below.Step-by-Step:
1
Find the exponent of the power. In our example, the exponent is 2.
2
Find the top number (called the numerator) of the fraction. In our example, the numerator is 3.
3
Raise the number found in Step 2 (3) to the exponent found in Step 1 (2). This becomes the numerator of the answer.
4
Find the bottom number (called the denominator) of the fraction. In our example, the denominator is 4.
5
Raise the number found in Step 4 (4) to the exponent found in Step 1 (2). This becomes the denominator of the answer.
6
Evaluate the power on the top of the fraction. In our example, evaluate 32.
32 = 3 × 3 = 9
7
Evaluate the power on the bottom of the fraction. In our example, evaluate 42.
42 = 4 × 4 = 16
Answer:
(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: 2n. It has a base of 2 with an exponent of n.
- The bottom of the fraction is a power: 3n. It has a base of 3 with an exponent of n.