Section 8-1: Zero and Negative Exponents

Objectives: (1) To understand that numbers in the real number system are represented in a variety of

equivalent forms(2) To add, subtract, multiply and divide exponential

expressions

Properties

• Zero Exponent Property– For every nonzero number a, a0 = 1• Examples

– 50 = 1 (-2)0 = 1 (-1.02)0 = 1 (1/2)0 = 1

• Negative Exponent Property– For every nonzero number a and integer n,

a-n= • Examples

– 6-4 = (-8)-1 =

na

1

46

1

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Converting Negative Exponents to Positive Exponents

• Step 1: Make every number with a negative exponent a fraction (easiest way to convert any number into a fraction is putting it over 1)

• Step 2: Move the number to the other side of the fraction bar and change the sign

• Step 3: If there are no numbers left on one side of the fraction bar, put a 1 to represent that there was a number there originally.

Examples of Converting Negative Exponents

• 4-3 • 1 _ 43

• 1 _____ 4 • 4 • 4• 1__ This is what we call 64 simplifying a power

Simplifying an Exponential Expression

Simplify the expression4yx-3

4yX3

• Use the definition of negative exponents

• Simplify

• We’re done!• Tada!

3

14

xy

Simplifying an Exponential Expression

Simplify the expression:1w-4

w4

• Move the w to the other side of the fraction bar

• You’re done! • Tada!

Evaluating Exponential Expressions

Evaulate:3m2t-2 for t = -3, m = 23m2

t2 3(2)2

(-3)2 3(4) 912 943

• 1st: Convert to positive exponents

• 2nd: Plug in values (put them in parenthesis)

• 3rd : Simplify

• You’re done

Real-World Problem Solving

• Population Growth:A biologist is studying green peach aphids (a bug). In

the lab, the population doubles every week. The expression 1000 • 2w models an initial population of 1000 insects after w weeks of growth.a. Evaluate the expression for w = 0. Then describe what

the value of the expression represents in the situation.b. Evaluate the expression for w = -3. Then describe what

the value of the expression represents in the situation.

Part A

1000 • 2w

1000 • 20

1000 • 11000

• Plug in 0 for w• Now evaluate

• What does 1000 represent?

• The initial number of aphids

Part B

1000 • 2w

1000 • 2-3

1000 •

1000 • 125

• Plug in -3 for w• Now evaluate

• What does 125 represent?

• The number of aphids 3 weeks ago

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32

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