# Introduction

• $a^2=a*a$
• $a^3=a*a*a$
• $a^4=a*a*a*a$
• etc…

Be careful NOT to get this mixed up, such that you think $a^3=3a$, since $3a=3*a$, NOT $a*a*a$!!! So remember, whereas:

• $3a=a+a+a$
• $a^3=a*a*a$

Instead of saying “$a$ to the power of 2″, we say “$a$ squared”. Similarly, instead of saying “$a$ to the power of 3″, we say “$a$ cubed”.

For powers, for example, $a^2$, $a$ is called the base, and 2 is called theexponent/index. Together, the base and exponent, are called the power.

Note that:

• $a^1=a$
• $a^0=1$

Now if we write $3a^2$, this means $3*a*a$

However, if we write $(3a)^2$, this means $(3a)*(3a)=9a^2=9*a*a$

This is based on BEDMAS, such that brackets (B) comes before exponents (E), so the brackets must be executed first!

When multiplying terms together, first multiply the numbers together, then the variables. For example, $4a*3a*a=(4*3)*(a*a*a)=12a^3$

Sometimes, you may get questions that ask you to substitute in powers. For example, for $a^2$, what is the value if $a=3$. In this example, $a^2=3^2=9$.