CHAPTER 66-1 INTEGER EXPONENTS

OBJECTIVES

• EVALUATE EXPRESSIONS CONTAINING ZERO AND INTEGER EXPONENTS.

• SIMPLIFY EXPRESSIONS CONTAINING ZERO AND INTEGER EXPONENTS.

INTEGERD

• YOU HAVE SEEN POSITIVE EXPONENTS. RECALL THAT TO SIMPLIFY 32, USE 3 AS A FACTOR 2 TIMES: 32 = 3 3 = 9.

But what does it mean for an exponent to be negative or 0? You can use a table and look for a pattern to figure it out.

INTEGER EXPONENTS

• WHEN THE EXPONENT DECREASES BY ONE, THE VALUE OF THE POWER IS DIVIDED BY 5. CONTINUE THE PATTERN OF DIVIDING BY 5.

INTEGER EXPONENTS

ZERO EXPONENT

Notice the phrase “nonzero number” in the

previous table. This is because 00 and 0 raised to

a negative power are both undefined. For

example, if you use the pattern given above the

table with a base of 0 instead of 5, you would get

0º = . Also 0–6 would be = . Since division by

0 is undefined, neither value exists.

APPLICATION

• ONE CUP IS 2–4 GALLONS. SIMPLIFY THIS EXPRESSION.

• SOLUTION:

gal is equal to

EXAMPLE

• A SAND FLY MAY HAVE A WINGSPAN UP TO 5–3 M. SIMPLIFY THIS EXPRESSION.

• SOLUTION:

EXAMPLE 2: ZERO AND NEGATIVE EXPONENTS

• A. 4–3

Simplify.

B. 70

7º = 1 Any nonzero number raised to the zero power is 1.

EXAMPLE 3A: EVALUATING EXPRESSIONS WITH ZERO AND NEGATIVE EXPONENTS

• EVALUATE THE EXPRESSION FOR THE GIVEN VALUE OF THE VARIABLES.

• SOLUTION:

x–2 for x = 4

EXAMPLE

• SIMPLIFY THE EXPRESSION FOR THE GIVEN VALUES OF THE VARIABLES.

–2a0b-4 for a = 5 and b = –3

EXAMPLE

• SIMPLIFY THE EXPRESSION FOR THE GIVEN VALUES OF THE VARIABLES.

for a = –2 and b = 6

INTEGERS

What if you have an expression with a negative

exponent in a denominator, such as ?

or

• AN EXPRESSION THAT CONTAINS NEGATIVE OR ZERO EXPONENTS IS NOT CONSIDERED TO BE SIMPLIFIED. EXPRESSIONS SHOULD BE REWRITTEN WITH ONLY POSITIVE EXPONENTS.

EXAMPLE

• SIMPLIFY.

A. 7w–4

B.

EXAMPLE

• SIMPLIFY