Finding Negative Exponents
(KS3, Year 7)
The LessonA power with a negative exponent is equal to the reciprocal of the power (1 over the power) with the exponent made positive. Imagine we have the number 2 with an exponent of -n. We put the whole power under 1 and remove the minus sign from the exponent. This is equal to 1⁄2n.
This is a laws of exponents.
How to Find Negative Exponents
QuestionUse the law of exponents to find the power with the negative exponent below.
Write the power from the question on the bottom of the fraction (called the denominator).
Remove the minus sign from the exponent. In our example, the exponent of −2 becomes 2.
As the final step, evaluate the power with the positive exponent.
Evaluate the power on the bottom of the fraction. In our example, evaluate 32.
32 = 3 × 3 = 9
Answer:We have found the negative exponent.
Understanding Finding a Negative ExponentLet us look at the rule for negative exponents:
- 2−n and 2n are powers.
- The bases of the powers are 2.
- The exponent of 2−n is −n and the exponent of 2n is n.
- The fraction 1⁄2n is the reciprocal of 2n.
Lesson SlidesThe slider below shows another real example of how to find negative exponents. Open the slider in a new tab
What Is an Exponent?An exponent tells you how many times a number or letter is multiplied by itself. An exponent is denoted by a raised number by the right hand side of the number (called the base) that is multiplied by itself. For example, 22 means that 2 is multiplied by itself 2 times:
22 = 2 × 2
What Is a Reciprocal?A reciprocal of a quantity (such as a letter or power) is 1 divided by the quantity.
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