2-4 Properties of Exponentspage 97

an is called a Power 거듭제곱a is the base. 밑n is the exponent. 지수we read it as a to the nth power or a to the n, or a to the power n

Remember::::: (page 99) Simplified Monomial• 

①there are no powers of powers②each base appears once

③fractions are also simplified④there are no negative exponents

This property states that for any real num-ber x,a,b, .

Example : 9*27=243

1.Product of Powers

Properties of Exponent

This property states that for any real num-ber x,a,b, and if x is not 0, then

Example :

2. Quotient of Powers

27

This property states that for any real num-ber x,a,b, and when x is not 0, then

Example :

Negative of Exponent (this is not included in the MS2 curriculum)

= =

What is ?

Zero to zeroth power is often said to be"an indeterminate form", because it could have several different values. 

Since x0 is 1 for all numbers x other than 0, it would be logical to define that 00 = 1.

But we could think of 00 also having the value 0, because zero to any power (other than the zero power) is zero. 

Also, the logarithm of 00 would be 0 × infinity, which is in itself an indeterminate form. So laws of logs wouldn't work with it. 

For our class, we will define it as 0

0 to any power is 0

𝟎𝟎=𝟎

TODAY : OPERATION OF POLYNOMIAL

Properties of Exponent

Power of Power

= (a x a -> x times) -> y times= a x a -> xy times

= a xy(a ) x

*When a is not 0

y

Why is it?

= = (2 x 2 x 2)==2 times= (2 x 2 x 2) (2 x 2 x 2)= 2 x 2 x 2 x 2 x 2 x 2 =64

This property states that for any real num-ber x,a,b, .

Example 1 : Example 2 : Prove example 1 :

Power of a Power

This property states that for any real num-ber x,y,a,b,

, y is not 0, and , x is not 0

Examples : ,

Power of a quotient(Negative exponents are not part of the MS2 curricu-lum)

Property Definition Examples

Product of Powers z4×z3=z4+3

76 ×7 2= 76+2

Quotient of Powers

Negative Exponent

Power of a Power

Power of a Product

Power of a Quotient

Zero Power

bab

a

xx

xx ,0

0,11

xx

xand

xx a

aaa

baba xxx

abba xx

aaa yxxy

0,10 xx

If

,0,

y

y

x

y

xa

aa

and

0,0,

yxx

yor

x

y

y

xa

aaa

4484

8235

3

5

,666

6xx

x

x

996

6 1,

3

13 b

b

3631231263232 ,444 xxx

2223333 ,822 qppqyyy

7

77

5

55

,b

a

a

b

x

y

x

y

17561928492034

180

0

Simplify 1. Using the Power of a Quotient, 2. Using the Power of a Product,

3. Using the power of a power, the answer is   

Example of using proper-ties

Simplify an expression

1 Try this question first!

Definition ofnegative exponent

Definition of exponents

Divide out commonfactors

Simplify~!

Simplify an expression

Definition of exponents

Divide out commonfactors

Simplify~!

Practice – page 101

1) 2)

4) Find an expression for the area of the circle

6x4A=πr2A=π(6x4)2A=π(62x8)A=36 π x8

5) 6) 7)

Equations involving variable exponents with the same base

Since they have the same base, the expo-nents are equal….. x=y+2

36=9𝑎

𝑎=3

Homework

Page 102Make any exponent positive #15

If you do the additional exercises on pages 103-104 the answers include problems where the exponents in the question were negative so either do them with negative exponents or skip them.