Ch 8: ExponentsB) Zero & Negative Exponents

Objective:

To simplify expressions involving negative exponents and zero exponents.

Zero Exponent

Any base (except 0) with an exponent of 0 equals 1

For example: x0 = 1, 20 = 1, 100 = 1, (5x)0 = 1

Negative Exponent

Any base containing an exponent with a negative value should be “flipped” to change the exponent to a positive value.

Definitions

x−2= 1

x2For example:

1

Follow the Pattern!

€

33

€

32

€

31

€

30

€

3−1

€

3−2

€

3−3

= 3 3 3= 3 3= 3

= 1

=

€

13

=

€

13

€

13

=

€

13

€

13

€

13

€

÷3

€

÷3

€

÷3

€

÷3

€

÷3

€

÷3€

×1

3

€

×1

3

€

×1

3

1) Write expression in fraction format2) Draw a fraction bar3) Evaluate each base one at a time4) Positive exponents stay on the same side of the fraction bar

Negative exponents move to the opposite side

Rules

Power to Power Rule

( )xa

=b

xab

Shortcuts apply to Negative Exponents

( )23

=-2

23(-2)

= 2-6

=

€

126

Example 1

€

3−1

€

45 ⎛ ⎝

⎞ ⎠

−1

€

13

€

54

Example 3 Example 4

Example 2

€

1

4−2 = = 16=

=

€

3x−2 = 3x2

31

1=

11 42

5-1

4-1

=41

51

= = 3 x2

€

xy−3

€

=xy3

Example 5

€

1

5a( )−2

€

=25a2

Example 6

Example 7 =

€

x −3y 2

7z−1 x3

y2

7

z

=1 (5a)2

=(5a)(5a)

=x y3

=x3

y2

7z1

Classwork

1)

€

(82 )−1

€

=1

6482

1

2)

€

23 • 5−2

€

=82555

222

3)

4)

€

3−2

2−3

€

2

5

⎛

⎝ ⎜

⎞

⎠ ⎟−2

33222

€

=8

9

=2255

€

=25

45-22-2

1

1

6)

y2

6 x

7)(6xy)2

1

8)b4

(2a-3)

€

6xy−2

€

(6xy)−2

€

(2a−3)2(b)−4

y2

1

x236=

(2a-3)=

2

b4a3

2a3

=4

a6b4

5)

€

3x −2

x2

31

1

1 (6xy)(6xy)

1=