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Powers with Negative Exponents

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definition

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

notes

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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