Indices law - law 6 - Multiplying powers = Add the powers

`a^ma^n=a^(m+n)` 

To remember this: try simple numbers you know first.

`2^2\times2^2 = 4\times4=16`

Is this the same as:

`2^(2+2)`

`2^4=2\times2\times2\times2=16`

So yes `2^2\times2^2=2^(2+2)`

So  `a^ma^n=a^(m+n)`

More examples

Example 1

What is        `2^3\times2^4` ?

                     `2^3\times2^4 = 2^(3+4)=2^7`  

Which equals  `2\times2\times2\times 2\times2\times2\times2`      

`= 128`

Example 2

What is `(x^4)(x^5)`

We know `x^(4+5)=x^9`

(or   `x\timesx\timesx\timesx\timesx\timesx\timesx\timesx\timesx=x^(4+5)=x^9` )