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

Holt Algebra Integer Exponents You have seen positive exponents. Recall that to simplify 3 2, use 3 as a factor 2 times: 3 2 = 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  5 5 Power Value – –2  5 5  5 5 5 5

Holt Algebra 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 Integer Exponents Base x Exponent Remember! 4

Holt Algebra Integer Exponents

Holt Algebra Integer Exponents Notice the phrase “nonzero number” in the previous table. This is because 0 0 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 Integer Exponents 2 –4 is read “2 to the negative fourth power.” Reading Math

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

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

Holt Algebra Integer Exponents Example 2: Zero and Negative Exponents Simplify. A. 4 –3 B. 7 0 C. (–5) –4 D. –5 –4

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

Holt Algebra 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

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

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

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

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

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

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

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

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

Holt Algebra Integer Exponents scientific notation Vocabulary

Holt Algebra 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 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 Integer Exponents

Holt Algebra Integer Exponents Find the value of each power of 10. Example 1: Evaluating Powers of 10 A. 10 –6 C B. 10 4

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

Holt Algebra Integer Exponents Your Turn 1 Find the value of each power of 10. a. 10 –2 c b ,000,000,0001,000,

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

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

Holt Algebra Integer Exponents Your Turn 2 Write each number as a power of 10. a. 100,000,000 b c

Holt Algebra 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 Integer Exponents Find the value of each expression. Example 3: Multiplying by Powers of 10 A  10 8 B. 467  10 –3

Holt Algebra Integer Exponents Your Turn 3 Find the value of each expression. a  ,340,000 b  10 –

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

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

Holt Algebra Integer Exponents Order the list of numbers from least to greatest. Example 5: Comparing and Ordering Numbers in Scientific Notation 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 Integer Exponents Order the list of numbers from least to greatest. Your Turn Example 5 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 Integer Exponents Pg. 449: 24 – 57 odd Pg. 455: 14 – 35 odd Homework