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

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32 Integer Exponents 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) Write each number as a power of the given base. –100 4 3 3. 64; base 4 (–3) 3 4. –27; base (–3)

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Page 1: 32 Integer Exponents 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)

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)

Page 2: 32 Integer Exponents 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)

32 Integer Exponents

Evaluate expressions containing zero and integer exponents.

Simplify expressions containing zero and integer exponents.

Learning Targets

Page 3: 32 Integer Exponents 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)

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

Page 4: 32 Integer Exponents 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)

32 Integer Exponents

Page 5: 32 Integer Exponents 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)

32 Integer Exponents

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

Page 6: 32 Integer Exponents 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)

32 Integer Exponents

Zero and Negative Exponents

Simplify.

A. 4–3

B. y0

yº = 1

C. (–5)–4

D. –5–4

Page 7: 32 Integer Exponents 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)

32 Integer Exponents

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

Page 8: 32 Integer Exponents 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)

32 Integer Exponents

On Your OwnSimplify.

a. 10–4

b. (–2)–4

c. (–2)–5

d. –2–5

Page 9: 32 Integer Exponents 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)

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.

Page 10: 32 Integer Exponents 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)

32 Integer Exponents

Simplify.

Example 1: Simplifying Expressions with Zero and Negative Numbers

A. 7w–4 B.

Page 11: 32 Integer Exponents 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)

32 Integer Exponents

Simplify.

C.

and

Page 12: 32 Integer Exponents 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)

32 Integer Exponents

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

Page 13: 32 Integer Exponents 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)

32 Integer Exponents

On your own Example 1

Simplify.

a. 2r0m–3

b.

c.

Page 14: 32 Integer Exponents 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)

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

Page 15: 32 Integer Exponents 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)

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.

Page 16: 32 Integer Exponents 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)

32 Integer Exponents

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

Page 17: 32 Integer Exponents 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)

32 Integer Exponents

On your own! Example 2

Evaluate the expression for the given value of the variable.

3b-3b b = -3

Page 18: 32 Integer Exponents 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)

32 Integer Exponents

On your own! Example 2

Evaluate the expression for the given values of the variables.

for a = –2 and b = 6

Page 19: 32 Integer Exponents 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)

32 Integer Exponents

Page 20: 32 Integer Exponents 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)

32 Integer Exponents

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

Page 21: 32 Integer Exponents 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)

32 Integer Exponents

Simplify.

Example 3: Finding Quotients of Powers

A. B.

Page 22: 32 Integer Exponents 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)

32 Integer Exponents

C.

Simplify.

D.

Page 23: 32 Integer Exponents 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)

32 Integer Exponents

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

Page 24: 32 Integer Exponents 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)

32 Integer Exponents

Check It Out! Example 1

Simplify.

c. d.