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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)

 

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Last revised on July 19, 2011 by Kim Seward.
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