32 integer exponents warm up evaluate each expression for the given values of the variables. 1. x 3...

32 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)

32 Integer Exponents

Evaluate expressions containing zero and integer exponents.

Simplify expressions containing zero and integer exponents.

Learning Targets

32 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

32 Integer Exponents

32 Integer Exponents

https://www.khanacademy.org/math/arithmetic/exponents-radicals/negative-exponents-tutorial/v/zero--negative--and-fractional-exponents

32 Integer Exponents

Zero and Negative Exponents

Simplify.

A. 4–3

B. y0

yº = 1

C. (–5)–4

D. –5–4

32 Integer Exponents

http://my.hrw.com/math11/math06_07/nsmedia/lesson_videos/alg1/player.html?contentSrc=7719/7719.xml

32 Integer Exponents

On Your OwnSimplify.

a. 10–4

b. (–2)–4

c. (–2)–5

d. –2–5

32 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.

32 Integer Exponents

Simplify.

Example 1: Simplifying Expressions with Zero and Negative Numbers

A. 7w–4 B.

32 Integer Exponents

Simplify.

C.

and

32 Integer Exponents

http://my.hrw.com/math11/math06_07/nsmedia/lesson_videos/alg1/player.html?contentSrc=7721/7721.xml

32 Integer Exponents

On your own Example 1

Simplify.

a. 2r0m–3

b.

c.

32 Integer Exponents

Example 2: 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

32 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.

32 Integer Exponents

http://my.hrw.com/math11/math06_07/nsmedia/lesson_videos/alg1/player.html?contentSrc=7720/7720.xml

32 Integer Exponents

On your own! Example 2

Evaluate the expression for the given value of the variable.

3b-3b b = -3

32 Integer Exponents

On your own! Example 2

Evaluate the expression for the given values of the variables.

for a = –2 and b = 6

32 Integer Exponents

32 Integer Exponents

https://www.khanacademy.org/math/arithmetic/exponents-radicals/exponent-properties/v/exponent-properties-involving-quotients

32 Integer Exponents

Simplify.

Example 3: Finding Quotients of Powers

A. B.

32 Integer Exponents

C.

Simplify.

D.

32 Integer Exponents

http://my.hrw.com/math11/math06_07/nsmedia/lesson_videos/alg1/player.html?contentSrc=6360/6360.xml

32 Integer Exponents

Check It Out! Example 1

Simplify.

c. d.