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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√(ar) = (n√a)r

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**Fractional Exponents (Powers and Roots)**

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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 (x4)³

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POWER OF PRODUCT RULE (2x4)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 = d2.27 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 = d2.27 e H = (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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6.1 – Rational Exponents Radical Expressions Finding a root of a number is the inverse operation of raising a number to a power. This symbol is the radical.

6.1 – Rational Exponents Radical Expressions Finding a root of a number is the inverse operation of raising a number to a power. This symbol is the radical.

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