7 1 Integer Exponents Objectives Evaluate expressions containing

7 -1 Integer Exponents Objectives Evaluate expressions containing zero and integer exponents. Simplify expressions containing zero and integer exponents. Holt Algebra 1

7 -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 Algebra 1 5 5 5 51 5 50 5– 1 5– 2

7 -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 Algebra 1

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. 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 Algebra 1

7 -1 Integer Exponents Reading Math 2– 4 is read “ 2 to the negative fourth power. ” Holt Algebra 1

7 -1 Integer Exponents Example 1: Application One cup is 2– 4 gallons. Simplify this expression. Holt Algebra 1

7 -1 Integer Exponents Your Turn 1 A sand fly may have a wingspan up to 5– 3 m. Simplify this expression. Holt Algebra 1

7 -1 Integer Exponents Example 2: Zero and Negative Exponents Simplify. A. 4– 3 B. 70 C. (– 5)– 4 D. – 5– 4 Holt Algebra 1

7 -1 Integer Exponents Simplify. a. 10– 4 b. (– 2)– 4 c. (– 2)– 5 d. – 2– 5 Holt Algebra 1 Your Turn 2

7 -1 Integer Exponents Example 3 A: Evaluating Expressions with Zero and Negative Exponents Evaluate the expression for the given value of the variables. x– 2 for x = 4 Holt Algebra 1

7 -1 Integer Exponents Example 3 B: Evaluating Expressions with Zero and Negative Exponents Evaluate the expression for the given values of the variables. – 2 a 0 b-4 for a = 5 and b = – 3 Holt Algebra 1

7 -1 Integer Exponents Your Turn 3 a Evaluate the expression for the given value of the variable. p– 3 for p = 4 Holt Algebra 1

7 -1 Integer Exponents Your Turn 3 b Evaluate the expression for the given values of the variables. for a = – 2 and b = 6 2 Holt Algebra 1

7 -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 not denominator, it is considered equivalent to to be thesimplified. same base with Expressions be exponent rewritten with positive the opposite should (positive) in theonly numerator. exponents. Holt Algebra 1

7 -1 Integer Exponents Example 4: Simplifying Expressions with Zero and Negative Numbers Simplify. A. 7 w– 4 Holt Algebra 1 B.

7 -1 Integer Exponents Example 4: Simplifying Expressions with Zero and Negative Numbers Simplify. C. Holt Algebra 1

7 -1 Integer Exponents Your Turn 4 Simplify. a. 2 r 0 m– 3 b. Holt Algebra 1 c.

7 -1 Integer Exponents Objectives Evaluate and multiply by powers of 10. Convert between standard notation and scientific notation. Holt Algebra 1

7 -1 Integer Exponents Vocabulary scientific notation Holt Algebra 1

7 -1 Integer Exponents The table shows relationships between several powers of 10. Each time you divide by 10, the exponent decreases by 1 and the decimal point moves one place to the left. Holt Algebra 1

7 -1 Integer Exponents The table shows relationships between several powers of 10. Each time you multiply by 10, the exponent increases by 1 and the decimal point moves one place to the right. Holt Algebra 1

7 -1 Integer Exponents Holt Algebra 1

7 -1 Integer Exponents Example 1: Evaluating Powers of 10 Find the value of each power of 10. A. 10– 6 Holt Algebra 1 B. 104 C. 109

7 -1 Integer Exponents Writing Math You may need to add zeros to the right or left of a number in order to move the decimal point in that direction. Holt Algebra 1

7 -1 Integer Exponents Your Turn 1 Find the value of each power of 10. a. 10– 2 0. 10 Holt Algebra 1 b. 105 1, 000 c. 1010 100, 000, 000

7 -1 Integer Exponents Reading Math If you do not see a decimal point in a number, it is understood to be at the end of the number. Holt Algebra 1

7 -1 Integer Exponents Example 2: Writing Powers of 10 Write each number as a power of 10. A. 1, 000 Holt Algebra 1 B. 0. 0001 C. 1, 000

7 -1 Integer Exponents Your Turn 2 Write each number as a power of 10. a. 100, 000 107 Holt Algebra 1 b. 0. 0001 10 -5 c. 0. 1 10 -2

7 -1 Integer Exponents You can also move the decimal point to find the value of any number multiplied by a power of 10. You start with the number rather than starting with 1. Multiplying by Powers of 10 Holt Algebra 1

7 -1 Integer Exponents Example 3: Multiplying by Powers of 10 Find the value of each expression. A. 23. 89 108 B. 467 10– 3 Holt Algebra 1

7 -1 Integer Exponents Your Turn 3 Find the value of each expression. a. 853. 4 105 85, 340, 000 b. 0. 163 10– 2 0. 00163 Holt Algebra 1

7 -1 Integer Exponents Scientific notation is a method of writing numbers that are very large or very small. A number written in scientific notation has two parts that are multiplied. The first part is a number that is greater than or equal to 1 and less than 10. The second part is a power of 10. Holt Algebra 1

7 -1 Integer Exponents Example 4 A: Astronomy Application Saturn has a diameter of about Its distance from the Sun is about 1, 427, 000 km. Write Saturn’s diameter in standard form. Write Saturn’s distance from the Sun in scientific notation. Holt Algebra 1

7 -1 Integer Exponents Reading Math Standard form refers to the usual way that numbers are written—not in scientific notation. Holt Algebra 1

7 -1 Integer Exponents Example 5: Comparing and Ordering Numbers in Scientific Notation Order the list of numbers from least to greatest. Step 1 List the numbers in order by powers of 10. Step 2 Order the numbers that have the same power of 10 Holt Algebra 1

7 -1 Integer Exponents Your Turn Example 5 Order the list of numbers from least to greatest. Step 1 List the numbers in order by powers of 10. Step 2 Order the numbers that have the same power of 10 Holt Algebra 1

7 -1 Integer Exponents Homework Pg. 449: 24 – 57 odd Pg. 455: 14 – 35 odd Holt Algebra 1