# Introduction

When multiplying powers you expand them out firstly:

$a^2*a^7$ $=(a*a)*(a*a*a*a*a*a*a)$ $=a^9$

Another example:

$9a^2*4a^2$ $=9*a*a*4*a*a$ $=36a^4$

# Difference between adding and multiplying exponents

With adding powers you have to add the coefficients if the expressions are the same.

However, for multiplying powers it’s like adding the little numbers at the top:

Adding powers: $10ab^2+5ab^2=15ab^2$

Multiplying powers: $10ab^2*5ab^2=50ab^4$

# Power of a power

$(a^5)^2=a^5*a^5=a^{5+5}=a^{10}$

Harder question, $4(2y^2.z^3)^3$

$=4*2y^2.z^3*2y^2.z^3*2y^2.z^3$

$=8y^2.z^3*2y^2.z^3*2y^2.z^3$

$=16y^4.z^6*2y^2.z^3$

$=32y^6.z^9$

# Distributive Laws

Example of distributive law:

$a(b + c)$

$=a*b+a*c$

$=ab+ac$

The distributive law is very useful in simplifying powers whilst reducing mistakes.

For example, $10ab^2+5ab^2=ab^2(10+5)=ab^2(15)=15ab^2$