SOLUTION: Simplify: <pre> ((x^(3/2))y^-3)^1/3 ----------- -------- ((x^(1/2))y^-6)^-1 </pre>

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Question 148114: Simplify:

((x^(3/2))y^-3)^1/3 -------------------- ((x^(1/2))y^-6)^-1

Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
Start with the given expression.

Distribute the outer exponents to the inner exponents. Remember, . So in our case the numerator goes from to and the denominator goes from to

Use the technique described above to distribute the exponents.

Multiply the exponents.

Reduce.

Now when we divide monomials, we simply subtract the exponents. So for example

Let's apply this technique to the problem:

Subtract the exponents.

Rewrite as

Combine the exponents.

Reduce.

Simplify

Now rewrite as

So simplifies to

In other words, where every variable is positive and or