5. Simplify. Express your answer using all positive exponents.

 

 

This exercise is done exactly like exercise 4 is done. The steps that one performs in exercise 4 can be performed in this situation where the exponents are fractions. First we multiplied the exponent on top of the parentheses times all the exponents inside the parentheses. In this case we should first express the 4 as 22.

 

 

 

After multiplying the fractional exponents we are left with

 

 

 

It should be helpful if we move our factors in the bottom across the fraction bar to change the signs of the exponents, and move like factors next to each other.

 

When we multiply powers of the same base, we add the exponents.

We can add and subtract fractions. Of course we need common denominators when we do so. We are in luck with the y's. Their exponents have common denominators, but with the z's we need to find common denominators for 4ths and 3rds.

1/3 - 5/4 = 4/12 - 15/12 = -11/12

We should move the factors with the negative exponents to the bottom of the fraction.

 

It is important to realize that if you can do a problem like #4 then you can do a problem like #5.

 

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