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7-1 Integer Exponents Warm Up(Add to Notes) Evaluate each expression for the given values of the variables. 1. x3y2 for x = –1 and y = 10 2. Holt Algebra 1 for x = 4 and y = (–7) –100 7-1 Integer Exponents 7-1 Integer Exponents Holt Algebra Holt Algebra 11 7-1 Integer Exponents Remember! Base x 4 Exponent Holt Algebra 1 7-1 Integer Exponents Holt Algebra 1 7-1 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. Holt Algebra 1 7-1 Integer Exponents Example 1: Application One cup is 2–4 gallons. Simplify this expression. cup is equal to Holt Algebra 1 7-1 Integer Exponents Example 2: Zero and Negative Exponents Simplify. A. 4–3 B. 70 7º = 1 C. (–5)–4 D. –5–4 Holt Algebra 1 Any nonzero number raised to the zero power is 1. 7-1 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 Algebra 1 7-1 Integer Exponents Simplify. a. 10–4 Check It Out! Example 2 b. (–2)–4 c. (–2)–5 d. –2–5 Holt Algebra 1 7-1 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. Evaluate exponent. Write the power in the denominator as a product. Evaluate the powers in the product. Holt Algebra 1 7-1 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. Evaluate expressions with exponents. 2 Holt Algebra 1 Write the power in the denominator as a product. Evaluate the powers in the product. Simplify. 7-1 Integer Exponents 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. Holt Algebra 1 7-1 Integer Exponents Example 4: Simplifying Expressions with Zero and Negative Numbers Simplify. A. 7w–4 Holt Algebra 1 B. 7-1 Integer Exponents Example 4: Simplifying Expressions with Zero and Negative Numbers Simplify. C. and Holt Algebra 1 7-1 Integer Exponents Check It Out! Example 4 Simplify. a. 2r0m–3 rº = 1 and b. Holt Algebra 1 c. . 7-1 Integer Exponents Lesson Quiz: Part I 1. A square foot is 3–2 square yards. Simplify this expression. Simplify. 2. 2–6 3. (–7)–3 4. 60 5. –112 Holt Algebra 1 1 –121 7-1 Integer Exponents Lesson Quiz: Part II Evaluate each expression for the given value(s) of the variables(s). 6. x–4 for x =10 7. Holt Algebra 1 for a = 6 and b = 3 7-1 Integer Exponents Warm-Up 1. A square foot is 3–2 square yards. Simplify this expression. Simplify. 2. 2–6 3. (–7)–3 4. 60 5. –112 Holt Algebra 1 1 –121