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# 7.4 Rational Exponents.

## Presentation on theme: "7.4 Rational Exponents."— Presentation transcript:

7.4 Rational Exponents

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.

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

Fractional Exponents (Powers and Roots)

Quick Review – Exponent Rules

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

PRODUCT OR POWER RULE HAVE TO HAVE THE SAME BASE

QUOTIENT OF POWER RULE HAVE TO HAVE THE SAME BASE

POWER OF POWER RULE (x4)³

POWER OF PRODUCT RULE (2x4)⁵

POWER OF QUOTIENT 2 RULE

RATIONAL EXPONENT RULE

RADICAL TO EXPONENT RULE

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

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

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

Continued h = d2.27 e H = (100)2.27 1.2

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

Let’s Try Some

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