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EXAMPLE 3

a. . 5. 80. 12. 16. 18. 216. =. 12 18. =. =. 6. 4. 4. 4. 3. 3. 3. 3. 80. b. . =. =. =. 2. 4. 5. EXAMPLE 3. Use properties of radicals. Use the properties of radicals to simplify the expression. Product property. Quotient property. . . 5. 5. 3. 3. 3.

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EXAMPLE 3

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  1. a. 5 80 12 16 18 216 = 12 18 = = 6 4 4 4 3 3 3 3 80 b. = = = 2 4 5 EXAMPLE 3 Use properties of radicals Use the properties of radicals to simplify the expression. Product property Quotient property

  2.  5 5 3 3 3  3 27  5 27 a. = = 3 = 3  135 EXAMPLE 4 Write radicals in simplest form Write the expression in simplest form. Factor out perfect cube. Product property Simplify.

  3.      7 7 8 4 8 4 5 5 5 5 5 5    5 5 5 28 28 32 = b. = = 2 EXAMPLE 4 Write radicals in simplest form Make denominator a perfect fifth power. 25 = 32 35 = 243 45 = 1024 Product property Simplify.

  4.     2 2 2 2 2 3 3 3 3 3 (1 + 7) a. 8 7 + = = 4 4 3 4 4 3       3 10 10 10 27 54 10 b. = = + (81/5) 2 – 3 (3 – 1)  – – c.  2 3 = = = 2 (81/5) (81/5) 10 12 2 = (2 +10) (81/5) EXAMPLE 5 Add and subtract like radicals and roots Indices must match! In this case each index is 4, so operation is allowed Simplify the expression.

  5. 3   5 3 24 2   3 250 + 40 3 5 4 4 4 27 3 3 3 3   5 5 3 5 2 for Examples 3, 4, and 5 GUIDED PRACTICE Simplify the expression. SOLUTION SOLUTION SOLUTION SOLUTION

  6. 3  43(y2)3 a. 4y2 = = = 3pq4 b. (27p3q12)1/3 271/3(p3)1/3(q12)1/3 = = = 3 4 4 4 3p(3 1/3)q(12 1/3)     n8 43 m4 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 EXAMPLE 6 Simplify expressions involving variables Simplify the expression. Assume all variables are positive.

  7. 5  = 5 4a8b14c5  4a5a3b10b4c5 5 5   a5b10c5 4a3b4 a. = = 5 ab2c  4a3b4 EXAMPLE 7 Write variable expressions in simplest form Write the expression in simplest form. Assume all variables are positive. Factor out perfect fifth powers. Product property Simplify.

  8. 3  xy = 3  x y 3 =  y9 y3 b. = x y8 x y 3 x y 3 = 3 y9 y8 y EXAMPLE 7 Write variable expressions in simplest form Make denominator a perfect cube. Simplify. Quotient property Simplify.

  9. 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 EXAMPLE 8 Add and subtract expressions involving variables Perform the indicated operation. Assume all variables are positive.

  10. 6xy 3/4 3x 1/2 y 1/2 3q3 3  27q9 5 2x1/2y1/4 –  w  w3 9w5 x10 y5 x2 y w 2w2  for Examples 6, 7, and 8 GUIDED PRACTICE Simplify the expression. Assume all variables are positive. SOLUTION SOLUTION SOLUTION SOLUTION

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