Numbers
Multiplying and Dividing by Powers
Numbers
Any 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 = 4cm2
2cm
2cm
Numbers
Instead of writing 2 x 2 (or the answer 4), in
maths we write a number that is going to be
squared like this:
2
2
We call this the
BASE number
Numbers
Instead of writing 2 x 2 (or the answer 4), in
maths we write a number that is going to be
squared like this:
2
2
And we call this
the POWER or
INDICES
Numbers
The same is true in algebra. When we need
to multiply a letter by itself instead of
writing
axa
we write
2
a
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If 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 = 43
7 x 7 x 7 x 7 x 7 x 7 = 76
Numbers
g x g x g = g3
What happens if we multiply g3 by g2?
Do we get…
2g5 or 2g6
or g5
or g6
IT ALL GETS SO CONFUSING!!!!
Numbers
We need to understand how this works
g3 = g x g x g
g2 = g x g
So g3 x g2 is the same as
gxgxg x gxg
Which is… 5
g
Numbers
From this we can now say that when
we multiply power numbers we
add the indices together:
12
4
8
2
2 x2 =
8
3
5
3
3 x3 =
t2 x t8 = t10
Numbers
If we add indices when we multiply
power numbers, what do we do when
we divide power numbers?
Subtract the indices!
28 ÷ 22 = 26
39 ÷ 34 = 35
T6 ÷ t4 = t2
Numbers
Just 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 = 1
Because 6 goes into 6 once, 6x6x6
(216) goes into 6x6x6 (216) once.
Any number divided by itself is 1.