How to solve fractional exponents.

- Simplifying fractional exponents
- Simplifying fractions with exponents
- Negative fractional exponents
- Multiplying fractional exponents
- Dividing fractional exponents
- Adding fractional exponents
- Subtracting fractional exponents

## Simplifying fractional exponents

The base b raised to the power of n/m is equal to:

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

*)*

^{n}#### Example:

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

2^{3/2} = ^{2}*√*(2^{3})
= 2.828

## Simplifying fractions with exponents

Fractions with exponents:

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

*a*/

^{n}*b*

^{n}#### Example:

(4/3)^{3} = 4^{3 }
/ 3^{3} = 64 / 27 = 2.37

## 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}

#### Example:

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}

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

## Multiplying fractional exponents

Multiplying fractional exponents with same fractional exponent:

*a ^{ n/m}* ⋅

*b*= (

^{ n/m}*a*⋅

*b*)

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

2^{3/2} ⋅ 3^{3/2} = (2⋅3)^{3/2}*
= *6^{3/2}* = *
*√*(6^{3}) = *√*216 = 14.7

Multiplying fractional exponents with same base:

*a ^{ n/m}* ⋅

*a*=

^{ k/j}*a*

^{ (n/m)+(k/j)}#### Example:

2^{3/2} ⋅ 2^{4/3} = 2^{(3/2)+(4/3)}* = *
7.127

Multiplying fractional exponents with different exponents and fractions:

*a ^{ n/m}* ⋅

*b*

^{ k/j}#### Example:

2^{3/2} ⋅ 3^{4/3} = *√*(2^{3}) ⋅^{
3}*√*(3^{4})* = *2.828 ⋅ 4.327* = *
12.237

## Multiplying fractions with exponents

Multiplying fractions with exponents with same fraction base:

(*a / b*)* ^{ n}* ⋅ (

*a /*

*b*)

*= (*

^{ m}*a / b*)

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

(4/3)^{3} ⋅ (4/3)^{2} = (4/3)^{3+2}
= (4/3)^{5} = 4^{5} / 3^{5} = 4.214

Multiplying fractions with exponents with same exponent:

(*a / b*)* ^{ n}* ⋅ (

*c / d*)

*= ((*

^{ n}*a / b*)⋅(

*c / d*))

^{ n}#### Example:

(4/3)^{3} ⋅ (3/5)^{3} = ((4/3)⋅(3/5))^{3} = (4/5)^{3} = 0.8^{3} = 0.8⋅0.8⋅0.8 = 0.512

Multiplying fractions with exponents with different bases and exponents:

(*a / b*)* ^{ n}* ⋅ (

*c /*

*d*)

^{ m}#### Example:

(4/3)^{3} ⋅ (1/2)^{2} = 2.37 / 0.25 = 9.481

## Dividing fractional exponents

Dividing fractional exponents with same fractional exponent:

*a ^{ n/m}* /

*b*= (

^{ n/m}*a*/

*b*)

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

3^{3/2} / 2^{3/2} = (3/2)* ^{3/2}
= 1.5^{3/2}
= √*(1.5

*) =*

^{3}*√*3.375 = 1.837

Dividing fractional exponents with same base:

*a ^{ n/m}* /

*a*=

^{ k/j}*a*

^{ (n/m)-(k/j)}#### Example:

2^{3/2} / 2^{4/3} = 2^{(3/2)-(4/3)}*
= *2^{(1/6)}* = *^{ 6}*√*2* =* 1.122

Dividing fractional exponents with different exponents and fractions:

*a ^{ n/m}* /

*b*

^{ k/j}#### Example:

2^{3/2} / 3^{4/3} = *√*(2^{3})
/^{ 3}*√*(3^{4})* = *2.828 / 4.327* = *
0.654

## Dividing fractions with exponents

Dividing fractions with exponents with same fraction base:

(*a / b*)* ^{n}* / (

*a /*

*b*)

*= (*

^{m}*a / b*)

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

(4/3)^{3} / (4/3)^{2} = (4/3)^{3-2} = (4/3)^{1} = 4/3 = 1.333

Dividing fractions with exponents with same exponent:

(*a / b*)* ^{n}* / (

*c / d*)

*= ((*

^{n}*a / b*)/(

*c / d*))

*((*

^{n}=*a⋅d / b⋅c*))

^{n}#### Example:

(4/3)^{3} / (3/5)^{3} = ((4/3)/(3/5))^{3} = ((4⋅5)/(3⋅3))^{3} = (20/9)^{3} = 10.97

Dividing fractions with exponents with different bases and exponents:

(*a / b*)* ^{ n}* / (

*c /*

*d*)

^{ m}#### Example:

(4/3)^{3} / (1/2)^{2} = 2.37 / 0.25 = 9.481

## Adding fractional exponents

Adding fractional exponents is done by raising each exponent first and then adding:

*a ^{n/m}* +

*b*

^{k/j}#### Example:

3^{3/2} + 2^{5/2} = √(3^{3}) + √(2^{5})
= √(27) + √(32) = 5.196 + 5.657 = 10.853

Adding same bases b and exponents n/m:

*b ^{n/m}* +

*b*= 2

^{n/m}*b*

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

4^{2/3} + 4^{2/3} = 2⋅4^{2/3} = 2 ⋅^{
3}√(4^{2}) = 5.04

## Subtracting fractional exponents

Subtracting fractional exponents is done by raising each exponent first and then subtracting:

*a ^{n/m}* -

*b*

^{k/j}#### Example:

3^{3/2} - 2^{5/2} = √(3^{3})
- √(2^{5}) = √(27) - √(32) = 5.196 - 5.657 =
-0.488

Subtracting same bases b and exponents n/m:

3*b ^{n/m}* -

*b*= 2

^{n/m}*b*

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

3⋅4^{2/3} - 4^{2/3} = 2⋅4^{2/3} = 2 ⋅^{
3}√(4^{2}) = 5.04

Currently, we have around 1976 calculators, conversion tables and usefull online tools and software features for students, teaching and teachers, designers and simply for everyone.

You can find at this page financial calculators, mortgage calculators, calculators for loans, calculators for auto loan and lease calculators, interest calculators, payment calculators, retirement calculators, amortization calculators, investment calculators, inflation calculators, finance calculators, income tax calculators, compound interest calculators, salary calculator, interest rate calculator, sales tax calculator, fitness & health calculators, bmi calculator, calorie calculators, body fat calculator, bmr calculator, ideal weight calculator, pace calculator, pregnancy calculator, pregnancy conception calculator, due date calculator, math calculators, scientific calculator, fraction calculator, percentage calculators, random number generator, triangle calculator, standard deviation calculator, other calculators, age calculator, date calculator, time calculator, hours calculator, gpa calculator, grade calculator, concrete calculator, subnet calculator, password generator conversion calculator and many other tools and for text editing and formating, downloading videos from Facebok (we built one of the most famous Facebook video downloader online tools). We also provide you online downloanders for YouTube, Linkedin, Instagram, Twitter, Snapchat, TikTok and other social media sites (please note we does not host any videos on its servers. All videos that you download are downloaded from Facebook's, YouTube's, Linkedin's, Instagram's, Twitter's, Snapchat's, TikTok's CDNs. We also specialise on keyboard shortcuts, ALT codes for Mac, Windows and Linux and other usefull hints and tools (how to write emoji online etc.)

There are many very usefull online free tools and we would be happy if you share our page to others or send us any suggestions for other tools which will come on your mind. Also in case you find any of our tools that it does not work properly or need a better translation - please let us know. Our tools will 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 all over the world.

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