NumbersMultiplying and Dividing by Powers

NumbersAny number (or letter) multiplied by itself will result in a square number.

2 x 2 = 4, 5 x 5 = 25

We call it a square number because …

Numbers…the area of a square is the length multiplied by the width, and these are always the same…obviously!

2cm x 2cm = 4cm22cm

2cm

NumbersInstead of writing 2 x 2 (or the answer 4), in maths we write a number that is going to be squared like this:

22

We call this the BASE number

NumbersInstead of writing 2 x 2 (or the answer 4), in maths we write a number that is going to be squared like this:

22

And we call this the POWER or INDICES

NumbersThe same is true in algebra. When we need to multiply a letter by itself instead of writing

a x a we write

a2

NumbersIf we have to multiply a number by itself 3 times, or 4 times , then the small number (the power or indices) increases to show us how many times we multiply the number by itself…

4 x 4 x 4 = 7 x 7 x 7 x 7 x 7 x 7 =

43

76

Numbersg x g x g = g3

What happens if we multiply g3 by g2? Do we get…

IT ALL GETS SO CONFUSING!!!!g5or 2g6 or2g5 or g6

NumbersWe need to understand how this works

g3 = g x g x gg2 = g x g

So g3 x g2 is the same asg x g x g x g x g

Which is… g5

NumbersFrom this we can now say that when

we multiply power numbers we add the indices together:

24 x 28 =33 x 35 = t2 x t8 =

212

38

t10

NumbersIf we add indices when we multiply

power numbers, what do we do when we divide power numbers?

Subtract the indices!28 ÷ 22 =39 ÷ 34 = T6 ÷ t4 =

26

35

t2

NumbersJust two things to be careful of.

1) y x y4 = y5

because we do not put a 1 next to a base number.

2) 63 ÷ 63 = 1Because 6 goes into 6 once, 6x6x6 (216) goes into 6x6x6 (216) once. Any number divided by itself is 1.