### Transcription of Exponent and Radical Rules (6.1, 6.2) Day 20

1 **Exponent** and **Radical** **Rules** ( , ) Day 20 Name: _____ Block: _____ Topic Definition/Rule Example(s) Multiplication xa xb=xa+b Power to a Power xa()b=xab Power of a Product ab()n=anbn Zero Exponents x0=1 Division xaxb=xa b Power of a Quotient xy n=xnyn **simplifying** 1. 2. 3. **simplifying** Exponents Step Method Example 1 Label all unlabeled exponents 1 2 Take the reciprocal of the fraction and make the outside **Exponent** positive. 3 Get rid of any inside parentheses. 4 Reduce any fractional coefficients. 5 Move all negatives either up or down. Make the exponents positive. 6 Combine all like bases. 7 Distribute the power to all exponents. Use properties of exponents to simplify the following expressions. f. g. h. 121/8 125/6 = i. (51/3 x1/4)3 = j. (26 46)-1/6 = k. = l. RATIONAL EXPONENTS QUESTION: What is the square root of a number?

2 Determine what number fits into the . a. 5 i 5 = 5 is the _____ of 25 b. 10 i 10 = 10 is the _____ of 100 c. x i x = _____ is the square root of _____ d. x3 i x3 = _____ is the square root of _____ e. x9 i x9 = _____ is the square root of _____ QUESTION: What does the square root of x mean? x i x = x1 is the square root of x. RULE: _____ FRACTIONAL **Exponent** RULE: For any real number a and integers n and m: _____ Examples: a. 161/2 = = 4 b. 271/3 = = 3 c. (-8)1/3 = = -2 d. (16)1/4 = = 2 RATIONAL EXPONENTS **Exponent** (numerator) x1/2 Base (x) Root (denominator) RADICALS Index Radicand Exponential Notation **Radical** Notation x1/2 x2/3 x3/4 am/n a-m/n RULE: EXAMPLES: Evaluate each of the following without the use of a calculator!

3 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. RULE: EXAMPLES: Evaluate each of the following without the use of a calculator! 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. A negative **Exponent** was slipped into that last problem! How did you deal with it? RULE: EXAMPLES: Evaluate each of the following without the use of a calculator! 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. Mad Math Minute! Name: _____ Date: _____ 1. x23 = _____ 2. x2()3 = _____ 3. x4()7 = _____ 4. x3()4 = _____ 5. x13 = _____ 6. 10012 = _____ 7. y13 = _____ 8. x34 = _____ 9. x32 = _____ 10. 4912 = _____ 11. x15 = _____ 12. x4 = _____ 13. x12 = _____ 14. 1612 = ____ 15. x35 = _____ 16. x51 = _____ 17. x15 3 = _____ 18. 432 = _____ RADICALS Warm Up Simplify the following square root and cube root expressions 1.

4 2. 3. 4. EXAMPLE ONE **simplifying** square roots with variables a) b) EXAMPLE TWO Rationalizing the denominator a) 563 b) 71+25 EXAMPLE THREE Multiplying **Radical** Expressions c) d) EXAMPLE FOUR Adding and Subtracting **Radical** Expressions a) b) c) PRACTICE 1. 2. 3. x11 4. 5. 6. Simplify using the **Exponent** **Rules** . (No decimals, keep as fractions) 1. 2. 3. 4. 5. (a3b 6)(a2b0) 6. 7. 8. 9. 1. 5. 6. 7. 9. 10. 12. 243 33 15. 6323 543 4. 2. 13. 53+7 14. 21 43 **Exponent** PROPERTIES EXAMPLE FOUR Re-write the **Radical** expression in exponential form. a) b) c) d) EXAMPLE FIVE Simplify the expression without using a calculator. a) b) c) d)