# simplifying numbers with exponents

#### kjdjean

##### New member
how do I simplify:

3 to the 10th power plus 3 to the 10th power plus 3 to the 10th power ??

#### chrisr

##### Full Member
$$\displaystyle 3^{10}+3^{10}+3^{10}=(3)3^{10}=3^13^{10}=3^{1+10}=3^{11}$$

#### kjdjean

##### New member
Thank you! You are the first of many that I have asked that showed me how to get the right answer.

#### chrisr

##### Full Member
It's based on the following.

The exponent is the number of three's that are multiplied together.

$$\displaystyle 3(3)3(3)=3^4$$

$$\displaystyle 3(3)=3^2$$

$$\displaystyle 3(3)3(3)3=3^5$$

When multiplying, we just line up all the three's.

$$\displaystyle 3^43^3=[3(3)3(3)][3(3)3]=3(3)3(3)3(3)3=3^7=3^{4+3}$$

the same strategy for other powers, or you could replace all the three's with another repeating number

$$\displaystyle 5^25^7=5^{2+7}=5^9$$

In your example, adding 3 of the same thing is multiplying it by 3.

$$\displaystyle 2+2+2=3(2)\ etc$$