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

Students will be able to: Simplify & Evaluate expressions containing zero and integer exponents.

Learning Targets

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

Write & Complete the table!

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

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

11 cup is gallon.

16

Holt Algebra 1

7-1 Integer Exponents

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

Holt Algebra 1

7-1 Integer 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

Simplify.

a. 10–4

b. (–2)–4

c. (–2)–5

d. –2–5

Holt Algebra 1

7-1 Integer 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

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

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

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

Simplify.A. 7w–4 B.

Holt Algebra 1

7-1 Integer Exponents

Simplify.

C. and

Holt Algebra 1

7-1 Integer Exponents

Simplify.

a. 2r0m–3

b.

c.

HWp.449/25-77odd, Day 2 P.450/78-97