Holt Algebra 1

7-1 Integer Exponents7-1 Integer Exponents

Holt Algebra 1

Warm UpWarm Up

Lesson PresentationLesson Presentation

Lesson QuizLesson Quiz

Holt Algebra 1

7-1 Integer Exponents

Warm UpEvaluate each expression for the given values of the variables.

1. x3y2 for x = –1 and y = 10

2. for x = 4 and y = (–7)

Write each number as a power of the given base.

–100

433. 64; base 4

(–3)34. –27; base (–3)

Holt Algebra 1

7-1 Integer Exponents

Evaluate expressions containing zero and integer exponents.

Simplify expressions containing zero and integer exponents.

Objectives

Holt Algebra 1

7-1 Integer Exponents

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.

3125 625 125 25 5

5

Power

Value

55 54 53 52 51 5–150 5–2

5 5 5

Holt Algebra 1

7-1 Integer Exponents

When the exponent decreases by one, the value of the power is divided by 5. Continue the pattern of dividing by 5.

Holt Algebra 1

7-1 Integer Exponents

Base

x

Exponent

Remember!

4

Holt Algebra 1

7-1 Integer Exponents

Holt Algebra 1

7-1 Integer Exponents

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.

Holt Algebra 1

7-1 Integer Exponents

2–4 is read “2 to the negative fourth power.”

Reading Math

Holt Algebra 1

7-1 Integer Exponents

Example 1: Application

One cup is 2–4 gallons. Simplify this expression.

cup is equal to

Holt Algebra 1

7-1 Integer Exponents

Check It Out! Example 1

A sand fly may have a wingspan up to 5–3 m. Simplify this expression.

5-3 m is equal to

Holt Algebra 1

7-1 Integer Exponents

Example 2: Zero and Negative Exponents

Simplify.

A. 4–3

B. 70

7º = 1Any nonzero number raised to the zero

power is 1.

C. (–5)–4

D. –5–4

Holt Algebra 1

7-1 Integer Exponents

In (–3)–4, the base is negative because the

negative sign is inside the parentheses. In –3–4

the base (3) is positive.

Caution

Holt Algebra 1

7-1 Integer Exponents

Check It Out! Example 2 Simplify.

a. 10–4

b. (–2)–4

c. (–2)–5

d. –2–5

Holt Algebra 1

7-1 Integer Exponents

Example 3A: Evaluating Expressions with Zero and Negative Exponents

Evaluate the expression for the given value of the variables.

x–2 for x = 4

Substitute 4 for x.

Use the definition

Holt Algebra 1

7-1 Integer Exponents

Example 3B: Evaluating Expressions with Zero and Negative Exponents

Evaluate the expression for the given values of the variables.–2a0b-4 for a = 5 and b = –3

Substitute 5 for a and –3 for b.Evaluate expressions with

exponents.Write the power in the

denominator as a product.

Evaluate the powers in the product.

Simplify.

Holt Algebra 1

7-1 Integer Exponents

Check It Out! Example 3a

Evaluate the expression for the given value of the variable.

p–3 for p = 4

Substitute 4 for p.

Evaluate exponent.

Write the power in the denominator as a product.

Evaluate the powers in the product.

Holt Algebra 1

7-1 Integer Exponents

Check It Out! Example 3b

Evaluate the expression for the given values of the variables.

for a = –2 and b = 6

2

Substitute –2 for a and 6 for b.

Evaluate expressions with exponents.

Write the power in the denominator as a product.

Evaluate the powers in the product.

Simplify.

Holt Algebra 1

7-1 Integer Exponents

What if you have an expression with a negative

exponent in a denominator, such as ?

or Definition of a negative exponent.

Substitute –8 for n.

Simplify the exponent on the right side.

So if a base with a negative exponent is in a denominator, it is equivalent to the same base with the opposite (positive) exponent in the numerator.

An expression that contains negative or zero exponents is not considered to be simplified. Expressions should be rewritten with only positive exponents.

Holt Algebra 1

7-1 Integer Exponents

Simplify.

Example 4: Simplifying Expressions with Zero and Negative Numbers

A. 7w–4 B.

Holt Algebra 1

7-1 Integer Exponents

Simplify.

Example 4: Simplifying Expressions with Zero and Negative Numbers

C.

and

Holt Algebra 1

7-1 Integer Exponents

Check It Out! Example 4

Simplify.

a. 2r0m–3

b.

c.

rº = 1 and .

Holt Algebra 1

7-1 Integer Exponents

Lesson Quiz: Part I

1. A square foot is 3–2 square yards. Simplify this

expression.

Simplify.

2. 2–6

3. (–7)–3

4. 60

5. –112

1

–121

Holt Algebra 1

7-1 Integer Exponents

Lesson Quiz: Part II

Evaluate each expression for the given value(s) of the variables(s).

6. x–4 for x =10

7. for a = 6 and b = 3