1. 7.4 Rational Exponents

2. 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.

3. 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

4. Fractional Exponents (Powers and Roots)

5. Quick Review – Exponent Rules

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

7. PRODUCT OR POWER RULE
HAVE TO HAVE THE SAME BASE

8. QUOTIENT OF POWER RULE
HAVE TO HAVE THE SAME BASE

9. POWER OF POWER RULE
(x4)³

10. POWER OF PRODUCT RULE
(2x4)⁵

11. POWER OF QUOTIENT 2 RULE

12. RATIONAL EXPONENT RULE

13. RADICAL TO EXPONENT RULE

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

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

16. 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

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

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

19. Let’s Try Some