Negative Exponents or Negative Powers at Algebra Den

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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