Martin-Gay, Beginning Algebra, 5ed 33

Exponents that are natural numbers are shorthand notation for repeating factors.

34 = 3 • 3 • 3 • 3

3 is the base

4 is the exponent (also called power)

Note by the order of operations that exponents are calculated before other operations.

Martin-Gay, Beginning Algebra, 5ed 44

Evaluate each of the following expressions.

34 = 3 • 3 • 3 • 3 = 81

(–5)2 = (– 5)(–5) = 25

–62 = – (6)(6) = –36

(2 • 4)3 = (2 • 4)(2 • 4)(2 • 4) = 8 • 8 • 8 = 512

3 • 42 = 3 • 4 • 4 = 48

Example:

a)

b)

c)

d)

e)

Martin-Gay, Beginning Algebra, 5ed 55

Simplify each of the following expressions.

32 · 34 = 36= (3 · 3) · (3 · 3 · 3 · 3) = 729

= 32+4

Example:

32 · 34 = 36 = 729

x4 · x5 = x4+5

z3 · z2 · z5 = z3+2+5

(3y2)(– 4y4) = 3 · y2 (– 4) · y4 = 3(– 4)(y2 · y4) = – 12y6

= x9

= z10

a)

b)

c)

d)

Martin-Gay, Beginning Algebra, 5ed 66

i) m

m nn

xx m n

x

1ii)

m

n n m

xn m

x x

Martin-Gay, Beginning Algebra, 5ed 77

Simplify the following expressions.

2

74

3

9

ab

ba 533 ba))((3 2714 ba4 7

2

9

3

a b

a b

Example:

3

5

w

w 5 3

1

w 2

1

w

a)

b)

c)

d)

Martin-Gay, Beginning Algebra, 5ed 88

Martin-Gay, Beginning Algebra, 5ed 99

Simplify each of the following expressions.

(23)3 = 29 = 512

(x4)2 = x8

= 23·3

= x4·2

Example:

a)

b)

Martin-Gay, Beginning Algebra, 5ed 1010

Martin-Gay, Beginning Algebra, 5ed 1111

a)

b)

Martin-Gay, Beginning Algebra, 5ed 1212

Martin-Gay, Beginning Algebra, 5ed 1313

a)

b)

Martin-Gay, Beginning Algebra, 5ed 1414

Martin-Gay, Beginning Algebra, 5ed 1515

a)

b)

c)

Martin-Gay, Beginning Algebra, 5ed 1616