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College Algebra
Answer/Discussion to Practice Problems

Tutorial 5: Rational Exponents



check markAnswer/Discussion to 1a

prob 1a


We are looking for the square root of 100 raised to the 1 power, which is the same as just saying the square root of 100. 

If your exponent's numerator is 1, you are basically just looking for the root (the denominator's exponent). 

Our answer is 10 since the square root of 100 is 10.



check markAnswer/Discussion to 1b

prob 1b



*Rewrite exponent 2/3 as a cube root being squared

*Cube root of -1/64 = -1/4


In this problem we are looking for the cube root of -1/64 squared.  Again, I think it is easier to do the root part first if possible.  The numbers will be easier to work with. 

The cube root of -1/64 is -4 and (-4) squared is 16.



check markAnswer/Discussion to 2a

prob 2a





check markAnswer/Discussion to 2b

prob 2b


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

*Square root of 16 = 4



check markAnswer/Discussion to 2c

prob 2c



* Divide like bases, sub. exp

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




Check markAnswer/Discussion to 3a

prob 3a


*Simplify exponent
*Rewrite exponent 3/2 as a square root of x cubed




buffalo top


Last revised on Dec. 6, 2009 by Kim Seward.
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