Integer Exponents

Learning Objective

Upo n compl etion, you shoul d be able to

Perform opera tions invol ving integer

exponents.

INTEGER EXPONENTS

Shortcut for w riting repeated products

( n copies of a, provided n is a posi tive

integer, a is the base, n is the exponent)

...

n

na a a a a a

43 3 3 3 3 81

3

2 2 2 2 8

Laws of Exponents

0

:

31,

4

Example

0 1, 0a a

0

3 54 1

Laws of Exponents

3

3

:

1 1 15

5 5 5 5 125

Example

1

, 0, 0nn

a a na

Laws of Exponents

1. p q p qa a a

5 3 5 3 8

:

2 2 2 2

Example

Let , 0 and , 0a b R p q Z

2 5 2 5 3

3 3 3 3 27

Laws of Exponents

2. p

p q

q

aa

a

55 3 2

3

:

22 2 4

2

Example

Laws of Exponents

3. p p pab a b

5 5 5 5

:

2 2 32

Example

c c c

Laws of Exponents

4.

p p

p

a a

b b

5 5

5

:

2 2 32

3 3 243

Example

Laws of Exponents

5. qp pqa a

4 43 4 3 3 4 12

:

2 2 16 16

Example

s s s s

Perform the indicated operation

and simplify.

2 31. 3 2 9 8 17

222. -3 2 9 4 5

22 2 2 2 43. 2 3 2 3 18x x x x x

3

4 2 104. st s t

Perform the indicated operation

and simplify.

22 3 5

4 1 2

25.

3

a b c

a b c

22 4 3

12 3 0

256.

9

x y z

x y z

1

1 27. 2 3

SUMMARY

p q p qa a a p

p qq

aa

a

( ) p p pab a b

( )p

pp

a a

b b

( )p q pqa a1nn

aa

0 1a

Time to practice! -

Simplify the following:

1 31

2

0 2

30 2 2

1 25 1

4 21. 3.

9 4

2. 4.

sm n

r s

xyz x yb f

b x y z