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I'm a beginner to maths and have trouble simplyfying the following function:

$$\frac{p^y \cdot (pq)^o}{p^{2y+o} \cdot q^{o-2}}$$

The final answer is

$$p^{-y} \cdot q^2$$

But I'm not sure how to get there.

Any help is appreciated.

1 Answers 1

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Here's the method in general, without actually working out your example. You should do that yourself to seal the concepts.

The intermediate goal is to get all the powers of p and q separated in both the numerator and denominator. In this case, it's almost there, with the exception of (pq)^o. So expand that first, using the principle (x*y)^a = x^a * y^a.

Then gather the p's and q's using the properties of multiplication and exponentiation, x^a * x^b = x^(a+b). Finally, match the p's in the numerator and denominator, likewise the q's, and using the principle x^a / x^b = x^(a-b) calculate the ultimate powers of p and q. Note that there are two ways you could handle the power of p in the final answer, since it is negative.

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    Thanks, the only problem I have now is that I do not know how to expend (pq)^o because this is being multiplied with p^y.. p^y * p^o * q^o is different than p^y * (p^o * q^o). I probably am missing something basic.2010-09-07
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    See my revision. There is a principle for that too.2010-09-07
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    Remember that multiplication is associative!2010-09-07