Simplifying Exponents

St. IvesO http://

www.youtube.com/watch_popup?v=wGxNTZTSOmg&vq=small

As I was going to St Ives. I met a man with seven wives. Each wife had seven sacks. Each sack had seven cats. Each cat had seven kits. Kits, cats, sacks, wives. How many were going to St. Ives? How Many were going the opposite way?

Vocabulary

75Base Exponent

Power

IT’S THE LAW

In this lesson we will be learning about the laws of exponents and how to use them when simplifying exponential equations. The following laws are…O Product lawO Quotient lawO Power lawO Powers with different basesO Zero exponentsO Negative exponents

THE MUST KNOWS x1 = x

Any number to the 1st power is always the base number

x0 = 1 Any number to the 0 power is always 1

x-n = 1/xn

Any number to a negative power turns the equation into a fraction

Great video for negative exponents:http://www.youtube.com/watch_popup?v=T13ffipNGyA&vq=medium#t=51

Product Law

xmxn = xm+n

When you are multiplying two powers with the same base you simply add them together.

EX: x5x7=(xxxxx)(xxxxxxx)=xxxxxxxxxxxx=x12

Quotient Law

= Xm-n When you are dividing two powers you do the opposite and subtract them.

EX: = x2

Powers Law

(xm)n = xmn

When you multiply one exponent to another, to simplify, multiply exponents.

EX: (x2)5= x2x2x2x2x2=(xx)(xx)(xx)(xx)(xx)=x10REVIEW: http://

www.youtube.com/watch_popup?v=VQsQj1Q_CMQ&vq=medium

Powers With Different Bases

(xy)n = xnyn

(x/y)n = xn/yn

O Different bases cannot be simplified unless exponents are equal.

OEX: x6y6=(xy)6

Simplifying

A power is in its simplest form when the laws and definitions of exponents cannot be applied.

Positive Exponents ONLY.

Ex:

Practice• (x2)0

• m4 x m-3

• J6/J2

• (a2)4

• a3b3

• (2x2)-4

• 3m5 x 2m2

• 4j3/2j6

• (3a3)6

• a6/b6