 # Exponents 8 th Grade Pre-Algebra. Real Numbers Rational Numbers: Any number that can be written as a fraction Integers Positive and negative whole numbers.

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Real Numbers Rational Numbers: Any number that can be written as a fraction Integers Positive and negative whole numbers and zero Irrational Numbers Any positive or negative nonrepeating or nonterminating decimal, such as ∏ or, that cannot be written as a fraction

Real Numbers Included in the set of real numbers are positive and negative fractions, decimals, and rational and irrational numbers. Real Numbers Rational Numbers: Any number that can be written as a fraction Integers Positive and negative whole numbers and zero Irrational Numbers Any positive or negative nonrepeating or nonterminating decimal, such as ∏ or, that cannot be written as a fraction

Identifying rational numbers Use your calculator to answer the following questions: 1. Find the square root of 7. Does it repeat? Does it end? Is it a rational or an irrational number? 2. Find. Is it rational or irrational? Is it an integer? 3. Is an integer an irrational number? 4. Is an integer a real number? 5. Is a real number? Is it rational or irrational?

Identify as rational or irrational 1. 5 π 2. 3. 4. -7.2 5. 6. 7. 9 + π 8. 1.0004 9. 10. 11.

Understanding Exponents Sometimes it is necessary to multiply a number times itself one or more times. There is a shorter way to write this type of muliplication. Ex. 7 x 7 x 7 x 7 x 7 can be written 7 5

Properties of Exponents Any base number raised to the exponent of 1 equals the base number. Any base number raised to the exponent of 0 equals 1.

Examples Rewrite the following problems using exponents. 1. 10 x 10 2. 12 x 12 x 12 3. 4 x 4 x 4 x 4 4. 9 x 9 x 9 5. 5 x 5 x 5 x 5 x 5 6.

Calculator Time Use a calculator to figure what product each number with an exponent represents. 1. (-8) 3 6. (-10) 2 2. 12 2 7. 3 5 3. 20 1 8. 10 4 4. 5 4 9. 4 3 5. 15 0 10. 16 2

Think backwards Express each of the following numbers as a base with an exponent. 1. 97. 1000 2. 168. 125 3. 279. 81 4. 3610. 81 5. 811. 64 6. 3212. 49

Simplify 1. 2. 3. 4.

Geometry Application The number of diagonals of an n-sided figure is. Use the formula to find the number of diagonals for a 5-sided figure.

Geometry Application Use the formula to find the number of diagonals in a 7-sided figure.

Challenge Write (3 2 ) 3.

HW Textbook p. 86 (14-26)

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