Exponents and Scientific Notation Chapter 7 Exponents and Scientific Notation

7-1 Zero and Negative Exponents

Vocabulary Power-The base and the exponent of an expression of the form aᴺ Exponent-A number that shows repeated multiplication. Base-A number that multiplied repeatedly

Vocabulary continued Simplify-To replace an expression with its simplest name of form. Evaluate-To substitute a given number for each variable, and the simplify. Scientific Notation-A number expressed in the form a x 10ᴺ, where n is an integer and 1<|a|<10.

5² What is an Exponent Power How to Say it What is the power? What is the base? What is the exponent? Power How to Say it 10² Ten squared or ten to the second power 9³ Nine cubed or nine to the third power 3⁴ Three to the fourth power 4⁵ Four to the fifth power

Evaluate 5² = 5 x 5 = 25 6³ = 7⁴ = 8⁵ =

Simplify numeric base with negative exponent Make a fraction (if not already a fraction) and move the exponent. - if the exponent is on top of the fraction, move to the bottom. - if the exponent is on the bottom of the fraction, move to the top. - exponent will then be positive Evaluate. 7¯² = 7¯² 1 = 1 7² = 1 49 1 4¯³ = 4³ = 64

Examples: Simplify Together 1. 1 5¯³ 2. 4¯³ 3. 4b¯³k⁵ On Your Own a. 8¯² b. 1 2¯⁴ c. 9a¯²x¯⁹

Simplify numeric base with zero exponent Zero as an Exponent: for every nonzero number a, aᴼ = 1 5ᴼ = 1 (-8)ᴼ = 1

Move a single variable base with a negative Negative Powers: parentheses attach the negative sign to the base number. -3³ = -1 x 3 x 3 x 3 = -27 (-3)³ = -3 x -3 x -3 = -27 (-3)² = -3 x -3 = 9

Examples: Evaluate Together -9³ 2. (-7)² 3. 1 −5¯³ On Your Own -9³ 2. (-7)² 3. 1 −5¯³ On Your Own a. (-10)¯² b. -6⁴

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