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 with the same bases next to each other.

 

 

When we multiply powers of the same base, we add the exponents, and when we divide powers of the same base, we subtract 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.

 

 

 

In addition to working on the exponents on the z's we also combine the exponents on the y's.

 

 

Finishing the arithmetic we get

 

 

The directions tell us to express the answer using nothing but positive exponents. If a factor has a negative exponent, we can move it across the fraction bar and change its sign.

 

 

22 is more simply expressed as 4, so the final answer would usually be expressed as

 

 

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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