The LessonA letter with an exponent of −1 is equal to the reciprocal of the letter (1 divided by the letter). Imagine we have the letter a with an exponent of −1. This is equal to 1⁄a.
This is a law of exponents.
How to Find an Exponent of −1 in AlgebraFinding an exponent of −1 in algebra is easy.
QuestionUse the law of exponents to find the power with an exponent of −1 below.
Find the letter or symbol that has an exponent of −1. In our example, the letter is x.
Write the letter from Step 1 (x) on the bottom of the fraction (called the denominator).
Answer:We have found an exponent of −1.
Understanding Finding an Exponent of −1 in AlgebraLet us look at the rule for an exponent of −1 in algebra:
- a −1 is a power.
- The base of the power is a.
- The exponent is −1.
- The fraction 1⁄a is the reciprocal of a.
Lesson SlidesThe slider below shows another real example of how to find an exponent of −1 in algebra. Open the slider in a new tab
What Is a Reciprocal?A reciprocal of a letter is 1 divided by the letter.
Reciprocal of a FractionThe reciprocal of a fraction just flips the fraction upside down.
Reciprocals with CoefficientsWhat if there is a number or other letter written in front of a letter with an exponent of −1?
The number or letter in front is a coefficient that is multiplying what comes after it. It goes on top of the fraction instead of 1.