Adding exponents

How to add exponents.

• Adding numbers with exponents
• Adding negative exponents
• Adding fractional exponents
• Adding variables with exponents

Adding numbers with exponents

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

aⁿ + b^m

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/b^m

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:

a^n/m + b^k/j

Example:

3^3/2 + 2^5/2 = √(3³) + √(2⁵) = √(27) + √(32) = 5.196 + 5.657 = 10.853

 

Adding same bases b and exponents n/m:

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

Example:

4^2/3 + 4^2/3 = 2⋅4^2/3 = 2 ⋅ ³√(4²) = 5.04

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

Example:

x² + x² = 2x²