6.2 Warm-up

Simplify the expression.

1. 43∙48 411

4

5

8

82. 89

3. 48 34

1530 4. 215

2080 5. 52

6.2 Apply Properties of Rational Exponents

4

3

9

2

9

5

4

6464 f.4

3

9

7

4

64

4

32

9

76

)2(

)2(

4

6

9

42

2

2 36

54

36

168

2

36

114

2 6

13

2 6

13 22 6

1

28

Notes 6.2

Properties of Radicals

Simplify the expression.

a. 123 183 12 183= = 2 ∙ 33 333222 = 6

b. 804

54

805

4= = 164 = 2

Write each expression in simplest form.

a. 1353 3 5333 3 53

b.6

4

816

6

4

81

6

6

22

3333

)2222

2222(

6

6

2

12966

Notes 6.2

Combining Radicals and Roots

Simplify the Expression

a. 104 1047+ = 104(1 + 7) = 1048

b. (81/5)2 + (81/5)10 = (81/5)(2 +10) = (81/5)12

233 23–=c. 543 – 23 = 23273 23– 23(3 – 1)= = 2 23

(Same as x + 7x = 8x)

d. 55 215225 5 210

Notes 6.2Simplify expressions involving variables

Simplify the expression.

a. 64y63 = 43(y2)33 433 (y2)33= = 4y2

b. (27p3q12)1/3 = 271/3(p3)1/3(q12)1/3 = 3p(3 1/3)q(12 1/3) = 3pq4

c. m4

n8

4=

m44

n84 =

m44

(n2)44=

mn2

d.14xy 1/3

2x 3/4 z –6= 7x(1 – 3/4)y1/3z –(–6) = 7x1/4y1/3z6

Notes 6.2Write the expression in simplest form.

a. 4a8b14c55 = 4a5a3b10b4c5

5

a5b10c55 4a3b45

=

4a3b45ab2c=

Factor out perfect fifth powers.

Product property

b.x

y8

3=

x

y8

y

y

3

=x y

y9

3

Make denominator a perfect cube.

Simplify.

x y3

y93=

x y3

y3=

Quotient property

Notes 6.2

Combining Variable Expressions.

Perform the indicated operation.

a.15 w +

35 w =

45 w=

15

+ 35 w

b. 3xy1/4 8xy1/4– = (3 – 8) xy1/4 = – 5xy1/4

12c. z2z53 – 54z23 = 12z 2z23 – 3z 2z23

(12z – 3z) 2z23=

9z 2z23=

Homework: p. 424: 3 – 64 EOP