# When can I add exponents?

##### 1 Answer
Apr 7, 2016

${x}^{a} \times {x}^{b} = {x}^{a + b}$

#### Explanation:

Exponents can be added when two of the same base are multiplied. That is, ${x}^{a} \times {x}^{b} = {x}^{a + b}$. For example:

• ${2}^{3} \times {2}^{5} = {2}^{3 + 5} = {2}^{8}$

• ${5}^{- 1} \times {5}^{1} = {5}^{- 1 + 1} = {5}^{0} = 1$

• ${7}^{\frac{1}{4}} \times {7}^{\frac{3}{4}} = {7}^{\frac{1}{4} + \frac{3}{4}} = {7}^{1} = 7$

Note that this does not apply when the bases are different.