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:

*a ^{n} + b^{m}*

For example:

1^{2} + 2^{4} = 1⋅1+2⋅2⋅2⋅2⋅ = 1+16 = 17

Adding same bases ** b** and exponents

**:**

*n**b ^{n} + b^{n} = 2b^{n}*

For example:

*8 ^{2} + 8^{2} = 2⋅8^{2} = 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/a^{n} + 1/b^{m}*

For example:

*2 ^{-2} + 3^{-5} = 1/2^{2} + 1/3^{4} = 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} = √(2^{4}) + √(3^{6}) = √(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}√(8^{2}) = ^{3}√(64) = 4

### Adding variables with exponents

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

*x ^{n} + x^{m}*

With same exponents:

*x ^{n} + x^{n} = 2x^{n}*

For example:

*x ^{3} + x^{3} = 2x^{3}*