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

2. EXAMPLE 1
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( /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

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

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

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

6. Write variable expressions in simplest form
EXAMPLE 3
Write variable expressions in simplest form
Write the expression in simplest form. Assume all variables are positive.
4a8b14c5 √ 5 =
4a5a3b10b4c5 √ 5
Factor out perfect fifth powers.
a5b10c5 √ 5
4a3b4 =
Product property
4a3b4 √ 5
ab2c =
Simplify.

7. EXAMPLE 4
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 =