1. Simplifying Exponents

2. St. Ives 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?

3. Vocabulary 75
Base
Exponent
Power

4. 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…
Product law
Quotient law
Power law
Powers with different bases
Zero exponents
Negative exponents

5. THE MUST KNOWS x1 = x x0 = 1 x-n = 1/xn
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:

6. 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

7. Quotient Law 𝑥𝑚 𝑥𝑛 = Xm-n
When you are dividing two powers you do the opposite and subtract them.
EX: 𝑥8 𝑥6 = 𝑥𝑥𝑥𝑥𝑥𝑥𝑥𝑥 𝑥𝑥𝑥𝑥𝑥𝑥 = x2

8. 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)=x10
REVIEW:

9. Powers With Different Bases
(xy)n = xnyn
(x/y)n = xn/yn
Different bases cannot be simplified unless exponents are equal.
EX: x6y6=(xy)6

10. Simplifying
A power is in its simplest form when the laws and definitions of exponents cannot be applied. Positive Exponents ONLY. Ex: 15𝑥2𝑦3𝑧5 18𝑥𝑦_2𝑧_4 = 5𝑥𝑦5𝑧9 6

12. Practice (x2)0 m4 x m-3 J6/J2 (a2)4 a3b3 (2x2)-4 3m5 x 2m2 4j3/2j6