1. 7/3/2015 11:50 AM10.2 - Rational Exponents1 WRITING RADICALS IN RATIONAL FORM Section 10.2

2. 7/3/2015 11:50 AM10.2 - Rational Exponents2 DEFINITIONS Base: The term/variable of which is being raised upon Exponent: The term/variable is raised by a term. AKA Power BASE EXPONENT

3. 7/3/2015 11:50 AM10.2 - Rational Exponents3 THE EXPONENT

4. 7/3/2015 11:50 AM10.2 - Rational Exponents4 NTH ROOT RULE M is the power (exponent) N is the root A is the base

5. 7/3/2015 11:50 AM10.2 - Rational Exponents5 RULES Another way of writing is 25 1/2. is written in radical expression form. 25 1/2 is written in rational exponent form. Why is square root of 25 equals out of 25 raised to ½ power?

6. 7/3/2015 11:50 AM10.2 - Rational Exponents6 EXAMPLE 1 Evaluate 4 3/2 in radical form and simplify.

7. 7/3/2015 11:50 AM10.2 - Rational Exponents7 EXAMPLE 1 Evaluate 4 3/2 in radical form and simplify.

8. 7/3/2015 11:50 AM10.2 - Rational Exponents8 EXAMPLE 2 Evaluate 4 1/2 in radical form and simplify.

9. 7/3/2015 11:50 AM10.2 - Rational Exponents9 YOUR TURN Evaluate (–27) 2/3 in radical form and simplify.

10. 7/3/2015 11:50 AM10.2 - Rational Exponents 10 EXAMPLE 3 Evaluate –27 4/3 in radical form and simplify. Hint: Remember, the negative is OUTSIDE of the base Use calculator to check

11. 7/3/2015 11:50 AM10.2 - Rational Exponents 11 EXAMPLE 4 Evaluate in radical form and simplify.

12. 7/3/2015 11:50 AM10.2 - Rational Exponents12 NTH ROOT RULE M is the power (exponent) N is the root A is the base DROP AND SWAP

13. 7/3/2015 11:50 AM10.2 - Rational Exponents13 EXAMPLE 5 Evaluate (27) –2/3 in radical form and simplify.

14. 7/3/2015 11:50 AM10.2 - Rational Exponents14 EXAMPLE 6 Evaluate (–64) –2/3 in radical form and simplify.

15. 7/3/2015 11:50 AM10.2 - Rational Exponents15 YOUR TURN Evaluate in radical form and simplify.

16. 7/3/2015 11:50 AM10.2 - Rational Exponents16 PROPERTIES OF EXPONENTS Product of a Power: Power of a Power: Power of a Product: Negative Power Property: Quotient Power Property:

17. 7/3/2015 11:50 AM10.2 - Rational Exponents17 EXAMPLE 7 Simplify Saying goes: BASE, BASE, ADD If the BASES are the same, ADD the powers

18. 7/3/2015 11:50 AM10.2 - Rational Exponents18 EXAMPLE 8 Simplify

19. 7/3/2015 11:50 AM10.2 - Rational Exponents19 YOUR TURN Simplify

20. 7/3/2015 11:50 AM10.2 - Rational Exponents20 EXAMPLE 9 Simplify Saying goes: POWER, POWER, MULTIPLY If the POWERS are near each other, MULTIPLY the powers – usually deals with PARENTHESES

21. 7/3/2015 11:50 AM10.2 - Rational Exponents21 EXAMPLE 10 Simplify

22. 7/3/2015 11:50 AM10.2 - Rational Exponents22 YOUR TURN Simplify

23. 7/3/2015 11:50 AM10.2 - Rational Exponents23 EXAMPLE 11 Simplify Saying goes: When dividing an expression with a power, SUBTRACT the powers.

24. 7/3/2015 11:50 AM10.2 - Rational Exponents24 EXAMPLE 12 Simplify

25. 7/3/2015 11:50 AM10.2 - Rational Exponents25 EXAMPLE 13 Simplify