Exponent Laws #4 and #5

These laws are generated (and understood) by extending

an accepted numerical pattern…

The second tier of the exponents laws takes us beyond the range of

“common visualization”

In generalx0 = 1

23 = 8

22 = 4

21 = 2 Continue the pattern

20 =

1 2

x

1 2

x

1 2

x 1

This law holds true for any number!

Any number to the exponent zero always reduces to 1

Continue the previous pattern..

Is there a pattern?

2-1 = 121

2-2 =12

12

X =

2-3 =12

X12

12

X =

1

22

1

23

In General

X-n = 1

• When given a negative exponent, invert the term and change the negative exponent to a positive exponent

Xn

For example:

2-3 = 123

= 18

35

-2

=53

2 53

=53

X

=259

3-2 =

132

=

19

(2x)3 = 8x3

(x4)(x3) = x7

(y4)5 = y20

Try some others