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Simplifying Expressions with Variables

Learn how to simplify expressions involving variables and apply various properties of exponents to simplify the expressions. Examples include simplifying radicals, factoring out perfect powers, and adding/subtracting variable expressions.

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Simplifying Expressions with Variables

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  1. 1. – 4 4 243 48 4 3 ANSWER WARM-UP PROBLEM Simplify the expression. Assume all variables are positive.

  2. 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 1 Simplify expressions involving variables Simplify the expression. Assume all variables are positive.

  3. √ 3 27q9 5 x10 y5 x2 y GUIDED PRACTICE Simplify the expression. Assume all variables are positive. 1. ANSWER 3q3 2. ANSWER

  4. 3 √ xy = 3 √ x y 3 = √ y9 y3 = x y8 x y 3 x y 3 = 3 y9 y8 y EXAMPLE 2 Write variable expressions in simplest form Make denominator a perfect cube. Simplify. Quotient property Simplify.

  5. 6xy 3/4 3x 1/2 y 1/2 GUIDED PRACTICE Simplify the expression. Assume all variables are positive. 3. ANSWER 2x1/2y1/4

  6. √ 5 = 5 4a8b14c5 √ 4a5a3b10b4c5 5 5 √ √ a5b10c5 4a3b4 = = 5 ab2c √ 4a3b4 EXAMPLE 3 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.

  7. 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 4 Add and subtract expressions involving variables Perform the indicated operation. Assume all variables are positive.

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