#   ```Name___________________________________ Date_______________
Period_________
RADICALS AND RATIONAL EXPONENTS WORKSHEET #2
REVIEW: nth Root: If b  a , then b is the n
n
th
root of a. This is written n
a  b . n is called the index of the radical. a is
1
m
th
called the radicand. Roots as Rational Exponents: The n root, n a , can be written as an exponent a n . a n 
 a
n
Notice the placement of the m and n. The root index is the denominator and the exponent is the numerator.
Simplify.
1)  121x 4
2)
81
144
3) 3 27a12
4) If f ( x)  4 x  1 ,
a) Find f(-2)
b) Find the domain of f(x)
Evaluate.
5) (27)
1
6) ( 16)
3
1
4
7) 16
3
4
Write in exponential form.
8)
5
9) ( 6 a ) 5
a2
Write as a radical expression with a smaller index.
10)
4
49
4
x
11)
14
x7
Simplify.
3
12)
x
13)
x2
4
x
14)
3
2
5
Use laws of exponents, reduce fractions, and write answers in simplified radical form.
4
13)
5
x3  x3
14)
5
4
x x
1
4
15)
x x
3

1
2
m
-
Use laws of exponents, reduce fractions, and write answers in simplified radical form.
 7
16)  4 y 8

  98 
  3 y 


 56 
19)  2 y 


22)
10
 53 
17)  y 
 
4
20) z

1


18)  3y 3 


1
2
21) z

4
3
9
2
5
a7
16a 4
a3
a
23)
4
7
6a
2
1
a2
1
1
25) x 3  x 4
24)
3
4
3
26) x 5  x

1
3
Simplify.
27)
10
30)
4
33)
25
28)
16x8
31)
9
27x 6
9
8
a3
29)
14
81
32)
6
y7
25x 4
```