1. 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( /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

2. 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.

3. 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.

4. 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 =

5. 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

6. 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