Exponents and Rules for Exponents

Standard Standard FormForm

Factored Factored FormForm

Exponential Exponential FormForm

1 =20

2 =2 =21

4 =2. 2 =22

8 =2. 2. 2 =23

16 =2. 2. 2 . 2 =24

Exponents:

Definition:

am = a.a.a.a.a…

“m” number of timesbase

exponent/power

Multiply the base times itself “m” times.

(0,1)

y=bx

a = a1

or 1a1 = aIf no exponent or coefficient – it is understood to be one.

Exponent RulePower of 1

Any number raised to the first power is equal to the number.

Any nonzero number raised to the zero power is 1.

a0 = 1

Exponent RulePower of 0

A negative exponent means to take the reciprocal of that number,

then raise it to the indicated power.

mm

aa

1

Exponent RuleNegative Powers

Exponent RuleNegative Powers

A negative exponent means to take the reciprocal of that number, then raise it to the indicated power.

For example, 5-2 is telling you to take the

reciprocal of 52 ( ), then square the 5( ).1

521

25

3

4

2 5

3 4

a b

c d

3

4

5 4

2 3

b d

a c=

**Short cut: If a negative exponent, move the base and exponent from the numerator to the denominator or vice versa.

Example:

Examples: Zero & Negative Exponents

1. 50

2. -30

3. (-6) 0

4. 5 x 100

5. 3-2

6.2

3

2

7. -3x0

8. -x0

9. (-4x)0

10. 3x0 + 4x0

11. (3x)0 + (4x)0

12. -2xy0

13. -14,285.70

= 1

= -1

= 1

=5

9

1

4

9

= -3

= -1

= 1

= 7

=2

= -2x

= -1

More Examples: Zero & Negative Exponents

13. 5ac-5

14.

15.

16.

3

7

1 5

2 4

a b

c d

4257

3

dcab

0

2)4(

b

16

1

32

4

8

3

ca

b

42

32

4

6

b

ca

5

5

c

a

Graphing Under a Restricted Domain

When graphing under a restricted domain, you will be given an interval of x values (domain). When graphing, only use values within this interval.

This will also restrict the y values (range). You will graph only a part of the exponential

function’s graph. No arrows on the graph to show that it continues.

For example, graph y = 2x under the domain {-3 < x < 3}.

Graphing Under a Restricted Domain (cont)

Graph these points and connect them.

x y-3 0.125-2 0.25-1 0.50 11 22 43 8

Domain: {-3 < x < 3}

Range: {.125 < y < 8}

{-3 < x < 3}

{.125 < y < 8}

The End