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6-1. Integer Exponents. Warm Up. Lesson Presentation. Lesson Quiz. Holt McDougal Algebra 1. Holt Algebra 1. Warm Up Evaluate each expression for the given values of the variables. 1. x 3 y 2 for x = –1 and y = 10 2. for x = 4 and y = (–7)

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6-1

Integer Exponents

Warm Up

Lesson Presentation

Lesson Quiz

Holt McDougal Algebra 1

Holt Algebra 1

Warm Up

Evaluate 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.

3. 64; base 4

4. –27; base (–3)

Objectives

Evaluate expressions containing zero and integer exponents.

Simplify expressions containing zero and integer exponents.

RECALL:

Positive exponents.

To simplify 32, use 3 as a factor 2 times: 32 = ???

VOCABULARY

Positive exponents

EXPONENT

BASE

 5

 5

 5

 5

ZERO OR NEGATIVE EXPONENTS

look for a pattern to figure it out.

55

54

53

52

51

50

5–1

5–2

625

3125

125

25

5

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

=

=

=

VOCABULARY

Zero Exponents – Any nonzero number raised to the zero power is 1.

Examples:

VOCABULARY

Negative Exponents– A nonzero number raised to a negative exponent is equal to 1 divided by that number raised to the opposite (postive) exponent.

Example:

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

gal is equal to

Example 1: Application

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

Try this one yourself!!!

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

TRY THESE YOURSELF!!!

Simplify.

A. 4–3

B. 70

7º = 1

C. (–5)–4

D. –5–4

E. (–2)–5

Caution

In (–5)–4, the base is negative because the negative sign is inside the parentheses. In –5–4the base (5) is positive.

Use the definition

Example 2

Evaluate the expression for the given value of the variables.

x–2 for x = 4

Substitute 4 for x.

Example 3: Try another yourself!!!

Simplify 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.

Simplify the denominator.

Simplify.

for a = –2 and b = 6

Try these yourself!!!

Evaluate the expression for the given value of the variable.

1.) p–3for p = 4

2.)

What if you have an expression with a negative exponent in a denominator, such as ?

*Move the denominator to the top and change the sign

**An answer with a negative exponent IS NOT simplified fully

B.

Example 4: Together

Simplify.

A. 7w–4

and

Example 4: Simplifying Expressions with Zero and Negative Numbers

Simplify.

C.

PRACTICE: ON YOUR OWN

Simplify.

a. 2r0m–3

b.

c.

6.1 HOMEWORK

PG. 395 - 397

#24-42(all), 44-66(evens), 78-83, 100