(Back to the tutorial on rational exponents)

Intermediate Algebra
Answer/Discussion to Practice Problems
on Rational Exponents


 

Answer/Discussion to 1a


 
*Rewrite exponent 1/5 as a fifth root

 
We are looking for the fifth root of 1/32 raised to the 1 power which is the same as just saying the fifth root of 1/32. 

Our answer is 1/2 since the fifth root of 32 is 2.

 
(return to problem 1a)

 


 
 

Answer/Discussion to 1b


 
*Rewrite exponent 3/4 as the fourth root being cubed

 
We are looking for the fourth root of 16 raised to the third power.

The fourth root of 16 is 2 and 2 cubed is 8.

 
(return to problem 1b)


 

Answer/Discussion to 1c


 
*Rewrite exponent 3/2 as the square root being cubed

 
We are looking for the opposite of the square root of 9/25 raised to the third power.

The square root of 9/25 is 3/5 and 3/5 cubed is 27/125.  Taking the opposite we get -27/125.

 
(return to problem 1c)


 

Answer/Discussion to 2a


 
*Rewrite as recipe. of base raised to pos. exp.
 

*Rewrite exponent 5/2 as the square root raised to the fifth power
 

 

 
We are looking for the square root of 9 raised to the fifth power.

The square root of 9 is 3 and 3 to the fifth power is 243.

 
(return to problem 2a)

 


 

Answer/Discussion to 3a


 

 
 
 
 

* Divide like bases, sub. exp
 

*Raise a base to two exponents, mult. exp.

*Rewrite as recip. of base raised to pos. exp.
 

 
(return to problem 3a)


 

Answer/Discussion to 3b


 

 

*Raise a base to two exponents, mult. exp.
 

 

 
(return to problem 3b)

 


 

Answer/Discussion to 4a


 

 

* Multiply like bases, add. exp
 

 

 
(return to problem 4a)


 

Answer/Discussion to 5a


 

 

*Factor out x to the 1/3

 
(return to problem 5a)

 


 

Answer/Discussion to 6a


 
*Rewrite ninth root of x cubed as x to the 3/9 power

*Simplify exponent

*Rewrite exponent 1/3 as a cube root
 

 
(return to problem 6a)

 

(Back to the tutorial on rational exponents)

All contents copyright (C) 2001 - 2008, WTAMU and Kim Seward. All rights reserved.
Last revised on Jan. 8, 2002 by Kim Seward.