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Home >> Exponents >> Negative Exponents >>

Negative Exponents or Negative Powers

Laws of Exponents Negative Exponents

Before you study what are negative exponents, you are advised to read:

What are exponents ?

As you must have already read exponential forms where power are natural number:
e.g. 23 = 2 X 2 X 2 = 8

But what happens when the exponent or power is negative:
e.g. 2-3
In such cases where the power is a negative integer, we do the inverse of the exponential form as shown below:
2-3 = 1/(2)3

Expand the exponential form and we get:
= 1/2 X 1/2 X 1/2

Solve multiplication expression and we get:
= 1/8

Hence, 2-3 = 1/8

Study the following examples to understand this concept further:

Example 1: Solve 10-5
Solution: As the given exponential form contains negative integer; so we do inverse of the exponential form and we get:
= 1/(10)5

Expand the exponential form and we get:
= 1/10 X 1/10 X 1/10 X 1/10 X 1/10

Solve multiplication expression and we get:
= 1/100000

Hence, 10-5 = 1/100000



Example 2: Solve 3-4
Solution: As the given exponential form contains negative integer; so we do inverse of the exponential form and we get:
= 1/(3)4

Expand the exponential form and we get:
= 1/3 X 1/3 X 1/3 X 1/3

Solve multiplication expression and we get:
= 1/81

Hence, 3-4 = 1/81


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