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6.2 Warm-up

2. 4. 5. 6.2 Warm-up. Simplify the expression. 1. 4 3 ∙4 8. 4 11. 8 9. 3. 6.2 Apply Properties of Rational Exponents. f. a. 5. 12. 18. 12 18. 80. 16. =. =. 2 ∙ 3. a. 3. 3. 3. 4. 4. 4. 80. b. =. =. =. 2. 4. 5. b. 3. . 135. Notes 6.2

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6.2 Warm-up

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  1. 2. 4. 5. 6.2 Warm-up Simplify the expression. 1. 43∙48 411 89 3.

  2. 6.2 Apply Properties of Rational Exponents

  3. f.

  4. a. 5 12 18 12 18 80 16 = = 2 ∙ 3 a. 3 3 3 4 4 4 80 b. = = = 2 4 5 b. 3  135 Notes 6.2 Properties of Radicals Simplify the expression. = 6 Write each expression in simplest form.

  5.     2 2 2 2 2 3 3 3 3 3 (1 + 7) a. 7 8 + = = 4 4 4 4 3 3       3 10 10 10 27 54 10 b. = = + (81/5) 2 – 3 (3 – 1)  – – c.  2 3 = = = 2 d. (81/5) (81/5) 12 10 2 = (2 +10) (81/5) Notes 6.2Combining Radicals and Roots Simplify the Expression (Same as x + 7x = 8x)

  6. 3  43(y2)3 a. 4y2 = = = 3pq4 b. (27p3q12)1/3 271/3(p3)1/3(q12)1/3 = = = 4 4 4 3 3p(3 1/3)q(12 1/3)     m4 43 n8 m4 m 3 3   (y2)3 64y6 14xy 1/3 4 7x1/4y1/3z6 7x(1 – 3/4)y1/3z –(–6) = = c. = = = n2 2x 3/4 z –6 4  (n2)4 d. m4 n8 Notes 6.2Simplify expressions involving variables Simplify the expression.

  7. 5 5 =  4a8b14c5  4a5a3b10b4c5 3  xy = 5 5   a5b10c5 4a3b4 a. 3  x y 3 =  y9 = y3 = b. = x 5 ab2c  4a3b4 y8 x y 3 x y 3 = 3 y9 y8 y Notes 6.2Write the expression in simplest form. Factor out perfect fifth powers. Product property Make denominator a perfect cube. Simplify. Quotient property

  8. 3z) (12z – 1 3 w w   + + 5 5 a. = = 9z 3 3   2z2 2z5 3 1 4 (3 – 8) xy1/4 – 5xy1/4 b. = = – 3xy1/4 8xy1/4 5 5 5 c. = z = 12 – w w   = 3 3 3 3 3z     – 2z2 2z2 54z2 2z2 12z Notes 6.2 Combining Variable Expressions. Perform the indicated operation. Homework: p. 424: 3 – 64 EOP

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