Adding exponents

 

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

 

See also

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