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.

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Warm Up Evaluate each expression for the given values of the variables. 1. x3y2 for x = –1 and y = 10 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.

You have seen positive 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. Power Value 55 54 53 52 51 50 5–1 5–2 3125 625 125 25 5  5  5  5  5

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

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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 ?
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.

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

Simplify. C. and

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

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

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.

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

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

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

Simplify. C. D.

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

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