#### Solved Examples and Worksheet for Converting Radical and Rational Exponent Form

Q1What is the radical form of x17 ?
A. 1x7
B. x7
C. x7
D. 7x7

Step: 1
x17 = x7
[Use the formula a1n = an .]
Q2What is the radical form of x910?
A. x910
B. x109
C. x1109
D. 110x9

Step: 1
x910 = (x9)110
Step: 2
= x910 or (x10)9
[Use the formula amn = amn or (an)m.]
Q3Express ( a7)6 in exponential form.

A. a76
B. a7
C. a67
D. a42

Step: 1
( a7)6 = (a17)6 = a67
[Use the formula amn = amn.]
Q4Express 3x9 in exponential form.

A. 3x9
B. (3x)9
C. (3x)19
D. 3 · x19

Step: 1
3x9 = (3x)19
[Use the formula abn = (ab)1n.]
Q5Express 3x- 78 in exponential form.

A. 318x18x
B. 318x18x2
C. 318x18x4
D. 38x18x

Step: 1
3x- 78 = (3x- 7)18
[Use the formula abn = (ab)1n.]
Step: 2
= 318x- 78
Step: 3
= 318x18x
Q6Express 7 x8 in exponential form.

A. (7x)18
B. 7x8
C. 7x18
D. x78

Step: 1
7 x8 = 7x18
[Use the formula an = a1n.]
Q7What is the radical form of the expression (16384)16?
A. 446
B. 16384
C. 46
D. 346

Step: 1
(16384)16 = 163846
[Use a1n = an.]
Step: 2
= (46 × 4)6
Step: 3
= 446
[Simplify.]
Q8Find the radical form of (10)18 ?
A. 105
B. 48
C. 58
D. 108

Step: 1
The radical form of (a)1n is an.
[Formula.]
Step: 2
The radical form of (10)18 is 108.
Q9Identify the radical form of the expression (625)23 ?

A. 5(53)2
B. 4(53)2
C. 25(53)2
D. 16(53)2

Step: 1
(625)23 = (6253)2
[Use a1n = an.]
Step: 2
= (53 × 5 3)2
[625 = 5 × 5 × 5 × 5 = 53 × 5.]
Step: 3
(553)2
[Simplify.]
Step: 4
= 25(53)2
[(ab)2 = a2b2.]
Q10What if the radical form of the expression (729)15

A. 3
B. 335
C. 3
D. 325

Step: 1
(729)15 = 7295
[Use a1n = an.]
Step: 2
= (35 × 3) 5
Step: 3
= 335
[Simplify.]