1. EXAMPLE 1
Find nth roots
Find the indicated real nth root(s) of a.
a. n = 3, a = –216
b. n = 4, a = 81
SOLUTION
a. Because n = 3 is odd and a = –216 < 0, –216 has one real cube root. Because (–6)3 = –216, you can write = 3√ –216 = –6 or (–216)1/3 = –6.
b. Because n = 4 is even and a = 81 > 0, 81 has two real fourth roots. Because 34 = 81 and (–3)4 = 81, you can write ±4√ 81 = ±3

2. Evaluate expressions with rational exponents
EXAMPLE 2
Evaluate expressions with rational exponents
Evaluate (a) 163/2 and (b) 32–3/5.
SOLUTION
Rational Exponent Form
Radical Form
a /2
(161/2)3 = 43 = 64 =
163/2
( )3  = 16 43 = 64 = = 1
323/5 = 1
(321/5)3 1
323/5 = 1
( )3 5  32 =
b –3/5
32–3/5 = 1 23 1 8 = = 1 23 1 8 =

3. Approximate roots with a calculator
EXAMPLE 3
Approximate roots with a calculator
Expression
Keystrokes
Display
a /5
b /8 7
c. ( )3 = 73/4 

4. GUIDED PRACTICE
for Examples 1, 2 and 3
Find the indicated real nth root(s) of a.
1. n = 4, a = 625
3. n = 3, a = –64.
SOLUTION ±5
SOLUTION –4
2. n = 6, a = 64
4. n = 5, a = 243
SOLUTION ±2
SOLUTION 3

5. GUIDED PRACTICE
for Examples 1, 2 and 3
Evaluate expressions without using a calculator.
5. 45/2 /4 27
SOLUTION 32
SOLUTION
–1/2
8. 17/8 1 3
SOLUTION
SOLUTION 1

6. GUIDED PRACTICE for Examples 1, 2 and 3
Evaluate the expression using a calculator. Round the result to two decimal places when appropriate.
Expression /5
SOLUTION
1.74 /3 –
SOLUTION
0.06
(4√ 16)5
SOLUTION 32
(3√ –30)2
SOLUTION
9.65