Finding a Power of a Fraction
(KS2, Year 6)
The LessonA power can have an fraction raised to an exponent.
This is a laws of exponents.
How to Find a Power of an Algebraic Fraction
QuestionUse 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.
For the final steps, evaluate the powers in our fraction.
Evaluate the power on the top of the fraction. In our example, evaluate 32.
32 = 3 × 3 = 9
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 FractionLet us look at the rule for powers of a fraction:
Firstly, let us look at what is to the left 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.
Lesson SlidesThe slider below shows another real example of how to find the power of a fraction. Open the slider in a new tab
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