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Using Exponential Notation

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3∙3∙3∙3∙3 can be written as 3 is a factor 5 times exponent Base Read as “three to the fifth power”

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ExpressionsIn Words 5²“five to the second power” or “five squared 5³“five to the third power” or “five cubed” 5⁴5⁴ “five to the fourth power”

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5 is the base to the exponent 4 Multiply -1 times four factors of 5 Parentheses indicate that -5 is the base to the exponent 4. Multiply four factors of -5 = (-5)(-5)(-5)(-5) = 625 An exponent applies only to its base. For example: Helpful Hint

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Don’t forget that 2 ⁴, for example, is not 2∙4. The expression 2⁴ means repeated multiplication of the same factor. 2⁴ = 2∙2∙2∙2 = 16 whereas 2∙4= 8

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Order of Operations 1. Perform all operations within parentheses( ), brackets [ ], or other grouping symbols such as fraction bars, starting with the innermost set. 2. Evaluate any expressions with exponents. 3. Multiply or divide in order from left to right. 4. Add or subtract in order from left to right P E M D A SP E M D A S

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Pg. 71-72 1-85 odd

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Evaluating Algebraic Expressions

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3 + x 5 ∙ y 2 ∙ z -1 + x x³

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Determine whether the given number is a solution to the equation. Substitute 5 for x. Simplify Right-hand side equals the left=hand side. Thus, 5 is a solution to the equation 4x = 20 4x = 20 x = 5

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Helpful Hint

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ADDITION: a + bSUBTRACTION: a - b The sum of a and b The difference of a and b a plus ba minus b b added to ab subtracted from a b more than aa decreased by b a increased by bb less than a the total of a and b

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Helpful Hint

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Multiplication: a ∙ bDivision: a ÷ b The product of a and b The quotient of a and b a times bA divided by b a multiplied by bb divided by a The ratio of a and b a over b a per b

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