Intermediate Algebra Tutorial 38


Intermediate Algebra
Answer/Discussion to Practice Problems
Tutorial 38: Rational Exponents

WTAMU > Virtual Math Lab > Intermediate Algebra > Tutorial 38: Rational Exponents


 

checkAnswer/Discussion to 1a

problem 1a
 

ad1a
*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)

 


 
 

checkAnswer/Discussion to 1b

problem 1b
 

ad1b
*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)


 

checkAnswer/Discussion to 1c

problem 1c
 

ad1c
*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)


 

checkAnswer/Discussion to 2a

problem 2a
 

ad2a
*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)

 


 

checkAnswer/Discussion to 3a

problem 3a
 

ad3a

 
 
 
 

* 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)


 

checkAnswer/Discussion to 3b

problem 3b
 

ad3b

 

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

 
 

(return to problem 3b)

 


 

checkAnswer/Discussion to 4a

problem 4a
 

ad4a

 

* Multiply like bases, add. exp
 

 
 

(return to problem 4a)


 

checkAnswer/Discussion to 5a

problem 5a
 

ad5a

 

*Factor out x to the 1/3
 

(return to problem 5a)

 


 

checkAnswer/Discussion to 6a

problem 6a
 

ad6a
*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)

 

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WTAMU > Virtual Math Lab >Intermediate Algebra >Tutorial 38: Rational Exponents


Last revised on July 19, 2011 by Kim Seward.
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