How to add 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 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 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 exponents is done by calculating each exponent first and then adding:
xn + xm
With same exponents:
xn + xn = 2xn
Example:
x2 + x2 = 2x2