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7.4 Rational Exponents

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I. Simplifying Expressions with Rational Exponents. Rational exponent – when there is a fraction as an exponent This is a different way of writing out a radical sign.

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How to interpret the fraction exponent: Denominator – this is the index of the radical sign Numerator – this is the power that the radicand is raised to, or you can raise the whole radical expression to a r/n = n √(a r ) = ( n √a) r

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Fractional Exponents (Powers and Roots) “Power” “Root”

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Quick Review – Exponent Rules

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NEGATIVE EXPONENT RULE Upstairs – Downstairs: A negative exponent means it’s in the wrong place.

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PRODUCT OR POWER RULE HAVE TO HAVE THE SAME BASE

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QUOTIENT OF POWER RULE HAVE TO HAVE THE SAME BASE

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POWER OF POWER RULE ( x 4 )³

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POWER OF PRODUCT RULE ( 2x 4 ) ⁵

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POWER OF QUOTIENT 2 RULE

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RATIONAL EXPONENT RULE

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RADICAL TO EXPONENT RULE

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Let’s put a few ideas together Convert the decimal to a fraction

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EX - simplify Need to Rationalize! Remember: We are ADDING exponents here – what do we need to add fractions? How did we get to here???

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7.4 Real-World Connection - Example 3 The optimal height h of the letters of a message printed on pavement is given by the formula h = 0.00252d 2.27 e Here d is the distance of the driver from the letters and e is the height of the driver’s eye above the pavement. All of the distances are in meters. Find h for the given value of d and e. d = 100 m; e = 1.2 m

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Continued h = 0.00252d 2.27 e H = 0.00252(100) 2.27 1.2

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Let’s Try Some Hint: convert to a fraction rather than a decimal!

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Let’s Try Some

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