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 + b^m

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:

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/b^m

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:

a^n/m + b^k/j

For example:

2^4/2 + 3^6/2 = √(2⁴) + √(3⁶) = √(16) + √(729) = 4 + 27 = 31

Adding same bases b and exponents n/m:

b^n/m + b^n/m = 2b^n/m

For example:

8^1/3 + 8^1/3 = 2⋅8^1/3 = 2 ⋅ ³√(8²) = ³√(64) = 4

Adding variables with exponents

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

xⁿ + x^m

With same exponents:

xⁿ + xⁿ = 2xⁿ

For example:

x³ + x³ = 2x³