Warm Up Evaluate each expression for the given values of the variables.

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. –100 3. 64; base 4 43 4. –27; base (–3) (–3)3

Learning Targets Evaluate expressions containing zero and integer exponents. Simplify expressions containing zero and integer exponents.

 5  5  5  5 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. 55 54 53 52 51 50 5–1 5–2 625 3125 125 25 5

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

Zero and Negative Exponents Simplify. A. 4–3 B. y0 yº = 1 C. (–5)–4 D. –5–4

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

On Your Own Simplify. a. 10–4 b. (–2)–4 c. (–2)–5 d. –2–5

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

B. Example 1: Simplifying Expressions with Zero and Negative Numbers Simplify. A. 7w–4

and Simplify. C.

On your own Example 1 Simplify. a. 2r0m–3 b. c.

Use the definition 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.

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.

On your own! Example 2 Evaluate the expression for the given value of the variable. 3b-3b b = -3

for a = –2 and b = 6 On your own! Example 2 Evaluate the expression for the given values of the variables.

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

Example 3: Finding Quotients of Powers Simplify. A. B.

Simplify. C. D.

Check It Out! Example 1 Simplify. c. d.

Warm Up Evaluate each expression for the given values of the variables.