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6-1 Integer Exponents Warm Up Evaluate each expression for the given values of the variables. 1. x3y2 for x = –1 and y = 10 2. –100 for x = 4 and y = (–7) Write each number as a power of the given base. 3. 64; base 4 43 4. –27; base (–3) Holt McDougal Algebra 1 (–3)3 6-1 Integer Exponents Remember! Base x 4 Exponent Holt McDougal Algebra 1 6-1 Integer Exponents Objectives Evaluate expressions containing zero and integer exponents. Simplify expressions containing zero and integer exponents. Holt McDougal Algebra 1 6-1 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. Power 55 54 53 52 Value 3125 625 125 25 5 Holt McDougal Algebra 1 5 5 5 51 5 50 5–1 5–2 6-1 Integer Exponents When the exponent decreases by one, the value of the power is divided by 5. Continue the pattern of dividing by 5. Holt McDougal Algebra 1 6-1 Integer Exponents Remember! Base x 4 Exponent Holt McDougal Algebra 1 6-1 Integer Exponents Reading Math 2–4 is read “2 to the negative fourth power.” Holt McDougal Algebra 1 6-1 Integer Exponents WORDS Zero exponent – Any nonzero number raised to the ______ exponent is _____. Negative exponent - nonzero number raised to a negative exponent is equal to _______ divided by that _____________ raised to the opposite (_____________) exponent. Holt McDougal Algebra 1 NUMBERS ALGEBRA 6-1 Integer Exponents Holt McDougal Algebra 1 6-1 Integer Exponents Notice the phrase “nonzero number” in the previous table. This is because 00 and 0 raised to a negative power are both undefined. For example, if you use the pattern given above the table with a base of 0 instead of 5, you would get 0º = . Also 0–6 would be = . Since division by 0 is undefined, neither value exists. Holt McDougal Algebra 1 6-1 Integer Exponents Example 1: Application One cup is 2–4 gallons. Simplify this expression. gal is equal to Holt McDougal Algebra 1 6-1 Integer Exponents Check It Out! Example 1 A sand fly may have a wingspan up to 5–3 m. Simplify this expression. 5-3 m is equal to Holt McDougal Algebra 1 6-1 Integer Exponents Example 2: Zero and Negative Exponents Simplify. A. 4–3 B. 70 7º = 1 C. (–5)–4 D. –5–4 Holt McDougal Algebra 1 Any nonzero number raised to the zero power is 1. 6-1 Integer Exponents Caution In (–3)–4, the base is negative because the negative sign is inside the parentheses. In –3–4 the base (3) is positive. Holt McDougal Algebra 1 6-1 Integer Exponents Simplify. a. 10–4 Check It Out! Example 2 b. (–2)–4 c. (–2)–5 d. –2–5 Holt McDougal Algebra 1 6-1 Integer Exponents Example 3A: 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 Holt McDougal Algebra 1 6-1 Integer Exponents Example 3B: Evaluating Expressions with Zero and Negative Exponents Simplify 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. Simplify the denominator. Simplify. Holt McDougal Algebra 1 6-1 Integer Exponents Check It Out! Example 3a Evaluate the expression for the given value of the variable. p–3 for p = 4 Substitute 4 for p. Simplify exponent. Write the power in the denominator as a product. Simplify the denominator. Holt McDougal Algebra 1 6-1 Integer Exponents Check It Out! Example 3b Evaluate the expression for the given values of the variables. for a = –2 and b = 6 Substitute –2 for a and 6 for b. Simplify expressions with exponents. Write the power in the denominator as a product. Simplify the denominator. 2 Holt McDougal Algebra 1 Simplify. 6-1 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. An ifexpression that contains exponent negative or zero So a base with a negative is in a exponents is it not to the be simplified. denominator, is considered equivalent to same base with Expressions be exponent rewritten with positive the opposite should (positive) in theonly numerator. exponents. Holt McDougal Algebra 1 6-1 Integer Exponents Example 4: Simplifying Expressions with Zero and Negative Numbers Simplify. A. 7w–4 Holt McDougal Algebra 1 B. 6-1 Integer Exponents Example 4: Simplifying Expressions with Zero and Negative Numbers Simplify. C. and Holt McDougal Algebra 1 6-1 Integer Exponents Check It Out! Example 4 Simplify. a. 2r0m–3 rº = 1 and b. Holt McDougal Algebra 1 c. .