# Powers with Negative Exponents

#### definition

Negative Exponent: A negative exponent means how many times to divide by the number.

# Powers with Negative Exponents:

A negative exponent means how many times to divide by the number.

103 = 10 × 10 × 10 = 1000

102 = 10 × 10 = 100

101 = 10 = 100/10

10° = 1 = 10/10

As the exponent decreases by 1, the value becomes one-tenth of the previous value.

10-1 = 1/10

10-2 = 1/10 ÷ 10 = 1/10 xx 1/10 = 1/100 = 1/10^2

10-3 = 1/100 ÷ 10 = 1/100 xx 1/10 = 1/1000 = 1/10^3.

In general, we can say that for any non-zero integer a, a- m = 1/a^m, where m is a positive integer. a- m is the multiplicative inverse of am.

## Integer with negative exponent:

2^(-3) = (1/2)^3

Step 1: Reciprocal of the integer 2 is 1/2.

Step 2: Negative exponent becomes a positive exponent.

## Fractions with negative exponents:

(2/7)^(-3) = (7/2)^3

Step 1: Reciprocal of the fraction 2/7 "is" 7/2.

Step 2: Negative exponent becomes a positive exponent.

#### Example

Find the multiplicative inverse of the following.
2– 4

2^(-4) = (1/2)^4

#### Example

Find the multiplicative inverse of the following.
10– 5

10– 5 = (1/10)^5.

#### Example

Find the multiplicative inverse of the following.

10– 100
10– 100 = (1/10)^(100)
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Powers having Negative Exponents [00:08:12]
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