EXAMPLE 6 Simplify expressions involving variables

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Presentation transcript:

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

Write variable expressions in simplest form EXAMPLE 7 Write variable expressions in simplest form Write the expression in simplest form. Assume all variables are positive. a. 4a8b14c5  5 = 4a5a3b10b4c5  5 Factor out perfect fifth powers. a5b10c5  5 4a3b4 = Product property 4a3b4  5 ab2c = Simplify. = x y8 y 3 b. x y8 3 Make denominator a perfect cube. = x y y9 3 Simplify.

Write variable expressions in simplest form EXAMPLE 7 Write variable expressions in simplest form x y  3 y9 = Quotient property x y  3 y3 = Simplify.

EXAMPLE 8 Add and subtract expressions involving variables Perform the indicated operation. Assume all variables are positive. a. 1 5  w + 3 = 1 5 + 3  w = 4 5  w b. 3xy1/4 8xy1/4 – = (3 – 8) xy1/4 = – 5xy1/4 12 c. z 2z5  3 – 54z2 = 12z 2z2  3 – 3z (12z – 3z) 2z2  3 = 9z 2z2  3 =

GUIDED PRACTICE for Examples 6, 7, and 8 Simplify the expression. Assume all variables are positive. 27q9  3 SOLUTION 27q9  3 = 33(q3)3  3 33  3 (q3)3 = = 3q3 x10 y5 5 SOLUTION = x10  5 y5 (x2)5 5  = y5 = x2 y x10 y5 5

GUIDED PRACTICE for Examples 6, 7, and 8 3x 1/2 y 1/2 6xy 3/4 SOLUTION 3x 1/2 y 1/2 6xy 3/4 = 2x(1 – 1/2)y(3/4 –1/2) = 2x1/2y1/4 w 9w5  – w3 SOLUTION w 9w5  – w3 = 32w2 w2 w  – w w2 w = 3w2  w w2 – = 2w2  w