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

$a^ma^n=a^(m+n)$

To remember this: try simple numbers you know first.

$10^2\times10^2 = 100\times100=10,000$

Is this the same as:

$10^(2+2)$

$10^4=10\times10\times10\times10=10,000$

So yes $10^2\times10^2=10^(2+2)$

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 $x\timesx\timesx\timesx\timesx\timesx\timesx\timesx\timesx=x^(4+5)=x^9$ )