Adding exponents

In this article we will learn how to add exponents.

Adding numbers with exponents

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

an + bm

For example:

12 + 24 = 1⋅1+2⋅2⋅2⋅2⋅ = 1+16 = 17

Adding same bases b and exponents n:

bn + bn = 2bn

For example:

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82 + 82 = 2⋅82 = 2⋅8⋅8 = 128

Adding negative exponents

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

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

For example:

2-2 + 3-5 = 1/22 + 1/34 = 1/(2⋅2)+1/(3⋅3⋅3⋅3) = 1/4+1/81 = 0.262345…

Adding fractional exponents

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

an/m + bk/j

For example:

24/2 + 36/2 = √(24) + √(36) = √(16) + √(729) = 4 + 27 = 31

Adding same bases b and exponents n/m:

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

For example:

81/3 + 81/3 = 2⋅81/3 = 2 ⋅ 3√(82) = 3√(64) = 4

Adding variables with exponents

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

xn + xm

With same exponents:

xn + xn = 2xn

For example:

x3 + x3 = 2x3

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