Algebra 21.8

Pinkston

5

6

5

6

9

. 2

. 2

. 4

. 4

. 4

A

B

C

D

E

SAT Question3 22 2Which of the following is equal to ?

x y x yb b b

2 5b b

Product of two equal bases with exponents:

Explanation:

(add exponents)

7( ) ( )b b b b b b b b

yx xyb b

5b

Power of a power:

Explanation:

(multiply exponents)

5 5 5 15b b b b

Power of a power:

hx y hx hya b a b (multiply exponents to each factor)

Quotient of two equal bases with exponents:

xx y

y

bb

b (subtract exponents)

Explanation:3

5

b

b

b b b

b b b b b

2b

2

1

b

Power of a quotient:

hx hx

y hx

a a

b b

thousands hundreds tens ones tenths hundredths

2 3 4 5 6 7

310

Remember the place value pattern for zero and negative exponents?

210 110 010 110 210

0 1x

3

3

x

x

Proofs:Further proof that

1 because anything divided by itself is 1.

3

3

x

x0x by the property of subtracting exponents.

0 1x Therefore,

3

5

x

x

Proofs:Further proof that

x x x

x x x x x

3

5

x

x2x by the property of subtracting exponents.

22

1x

x Therefore,

1bb

xx

by cancelling2

1

x

Order of Operations: PEMDAS (Please excuse my dear Aunt Sally)Parentheses, Exponents, Multiply & Divide (left to right), Add & Subtract

(left to right)

Classwork: 4-44 even evens,

48, 50 / 42-43

Get ready for a “Small Quiz” to be written

on your grade sheet.

Simplify without negative exponents:

Quiz. Copy the problems and write the answer.

Put your grade paper on the front of your row, quiz side down.

32. (4 )m

5 21. a b c 13. 10

THE END