Adding exponents

How to add exponents.

Adding numbers with exponents

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

an + bm

Example:

42 + 25 = 4⋅4+2⋅2⋅2⋅2⋅2 = 16+32 = 48

Adding same bases b and exponents n:

bn + bn = 2bn

Example:

42 + 42 = 2⋅42 = 2⋅4⋅4 = 32

Adding negative exponents

Adding negative exponents is done by calculating each exponent first and then adding:

a-n + b-m = 1/an + 1/bm

Example:

4-2 + 2-5 = 1/42 + 1/25 = 1/(4⋅4)+1/(2⋅2⋅2⋅2⋅2) = 1/16+1/32 = 0.09375

Adding fractional exponents

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

an/m + bk/j

Example:

33/2 + 25/2 = √(33) + √(25) = √(27) + √(32) = 5.196 + 5.657 = 10.853

 

Adding same bases b and exponents n/m:

bn/m + bn/m = 2bn/m

Example:

42/3 + 42/3 = 2⋅42/3 = 2 ⋅ 3√(42) = 5.04

Adding variables with exponents

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

xn + xm

With same exponents:

xn + xn = 2xn

Example:

x2 + x2 = 2x2


Currently, we have around 929 calculators and conversion tables to help you "do the math" quickly in areas such as:

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.


This website uses cookies to improve your experience, analyze traffic and display ads. Learn more