How to calculate negative exponents.

- Negative exponents rule
- Negative exponent example
- Negative fractional exponents
- Fractions with negative exponents
- Multiplying negative exponents
- Dividing negative exponents

## Negative exponents rule

The base b raised to the power of minus n is equal to 1 divided by the base b raised to the power of n:

*b ^{-n}* = 1 /

*b*

^{n}## Negative exponent example

The base 2 raised to the power of minus 3 is equal to 1 divided by the base 2 raised to the power of 3:

2^{-3} = 1/2^{3} = 1/(2⋅2⋅2) = 1/8 = 0.125

## Negative fractional exponents

The base b raised to the power of minus n/m is equal to 1 divided by the base b raised to the power of n/m:

*b*^{-n/m} = 1 /* b*^{n/m} = 1 /* *
(^{m}√*b*)^{n}

The base 2 raised to the power of minus 1/2 is equal to 1 divided by the base 2 raised to the power of 1/2:

2^{-1/2} = 1/2^{1/2} = 1/*√*2
= 0.7071

## Fractions with negative exponents

The base a/b raised to the power of minus n is equal to 1 divided by the base a/b raised to the power of n:

(*a*/*b*)^{-n} = 1 /
(*a*/*b*)^{n} = 1 / (*a*^{n}/*b*^{n})
= *b*^{n}/*a*^{n}

The base 2 raised to the power of minus 3 is equal to 1 divided by the base 2 raised to the power of 3:

(2/3)^{-2} = 1 / (2/3)^{2} = 1 / (2^{2}/3^{2})
= 3^{2}/2^{2 }= 9/4 = 2.25

## Multiplying negative exponents

For exponents with the same base, we can add the exponents:

*a ^{ -n}* ⋅

*a*=

^{ -m}*a*

^{ -(n+m}^{) }= 1 /

*a*

^{ n+m}#### Example:

2^{-3} ⋅ 2^{-4} = 2^{-(3+4)}
= 2^{-7} = 1 / 2^{7} = 1 / (2⋅2⋅2⋅2⋅2⋅2⋅2) = 1 / 128
= 0.0078125

When the bases are diffenrent and the exponents of a and b are the same, we can multiply a and b first:

*a ^{ -n}* ⋅

*b*= (

^{ -n}*a*⋅

*b*)

^{ -n}#### Example:

3^{-2} ⋅ 4^{-2} = (3⋅4)^{-2}
= 12^{-2} = 1 / 12^{2} = 1 / (12⋅12) = 1 / 144 =
0.0069444

When the bases and the exponents are different we have to calculate each exponent and then multiply:

*a ^{ -n}* ⋅

*b*

^{ -m}#### Example:

3^{-2} ⋅ 4^{-3} = (1/9) ⋅ (1/64) = 1
/ 576 = 0.0017361

## Dividing negative exponents

For exponents with the same base, we should subtract the exponents:

*a ^{ n}* /

*a*=

^{ m}*a*

^{ n-m}#### Example:

2^{6} / 2^{3} = 2^{6-3} = 2^{3} = 2⋅2⋅2 =
8

When the bases are diffenrent and the exponents of a and b are the same, we can divide a and b first:

*a ^{ n}* /

*b*= (

^{ n}*a / b*)

^{ n}#### Example:

6^{3} / 2^{3} = (6/2)^{3} =
3^{3} = 3⋅3⋅3 = 27

When the bases and the exponents are different we have to calculate each exponent and then divide:

*a ^{ n}* /

*b*

^{ m}#### Example:

6^{2} / 3^{3} = 36 / 27 = 1.333

Currently, we have around 935 calculators, conversion tables and usefull online tools and features to make your life easier or simply help you to do your work or duties faster and in more effective way. These below are the most commonly used by many users at all

- Free online calculators and tools
- Free online units conversion tools
- Free online web design tools
- Free online electricity & electronics tools
- Mathematics
- Online Tools
- Text Tools
- PDF Tools
- Code
- Ecology
- Numbers
- Algebra
- Trigonometry
- Probability & Statistics
- Calculus & analysis
- Mathematical symbols
- Addition table
- e constant
- Exponent rules
- Adding exponents
- Dividing exponents
- Fractional exponents
- Multiplying exponents
- Negative exponents
- Simplifying exponents
- Zero exponents
- Fibonacci numbers & sequence
- How e = 2.71828183 ?
- Multiplication table
- Printable multiplication table of 12x12
- Blank printable multiplication table of 12x12
- Printable multiplication table of 10x10
- Blank printable multiplication table of 10x10
- Multiplication table of 12x12
- Multiplication table of 10x10
- Numeral systems
- Parts-per million (ppm)
- Per-mille (‰)
- Percentage (%)
- Prime numbers
- Zero number (0)

And we are still developing more. Our goal is to become the one-stop, go-to site for people who need to make quick calculations or who need to find quick answer for basic conversions.

Additionally, we believe the internet should be a source of free information. Therefore, all of our tools and services are completely free, with no registration required. We coded and developed each calculator individually and put each one through strict, comprehensive testing. However, please inform us if you notice even the slightest error – your input is extremely valuable to us. While most calculators on Justfreetools.com are designed to be universally applicable for worldwide usage, some are for specific countries only.