Simplifying fractions with exponents

**HeidiHectic** · April 15th 2009, 05:09 PM

I have to simplify this and im totally confused step by step help would be so much appreciated!
$ \left( \frac {-6x^2y}{2xy^3} \right)^3 $

**Reckoner** · April 15th 2009, 05:21 PM

Originally Posted by HeidiHectic

I have to simplify this and im totally confused step by step help would be so much appreciated!
$ \left( \frac {-6x^2y}{2xy^3} \right)^3 $

Have you made any attempt at the problem? You should be familiar with these properties of exponentiation:

$(ab)^n=a^nb^n$

$\left(\frac ab\right)^n=\frac{a^n}{b^n}$

$a^{-n}=\frac1{a^n}$

$a^ma^n=a^{m+n}$

$\frac{a^m}{a^n}=a^{m-n}$

(where $a,\,b,\,m$ and $n$ have values such that the above expressions are defined)

Note that a variable without an exponent can be thought of as being raised to the 1st power.

**HeidiHectic** · April 15th 2009, 05:29 PM

yes, i understand those im just not sure what to do after you distribute the exponent.

**Reckoner** · April 15th 2009, 05:36 PM

Originally Posted by HeidiHectic

yes, i understand those im just not sure what to do after you distribute the exponent.

$\left(\frac{-6x^2y}{2xy^3}\right)^3$

$=\frac{-216x^6y^3}{8x^3y^9}$

$=\frac{-216}{8}\cdot\frac{x^6}{x^3}\cdot\frac{y^3}{y^9}$

$=\frac{-27\cdot8}{8}\cdot\frac{x^6}{x^3}\cdot\frac{y^3}{y^ 9}$

Now can you see how to continue?

**e^(i*pi)** · April 15th 2009, 05:40 PM

Originally Posted by HeidiHectic

I have to simplify this and im totally confused step by step help would be so much appreciated!
$ \left( \frac {-6x^2y}{2xy^3} \right)^3 $

I'd cancel a factor of 2, x and y before cubing

$ \left( \frac {-3x}{y^2} \right)^3 = \frac{-27x^3}{y^6} $

**Reckoner** · April 15th 2009, 05:40 PM

Originally Posted by e^(i*pi)

but 6^3 is 216?

That's funny. Where did I get 36? It is a mystery.

Originally Posted by e^(i*pi)

I'd cancel a factor of 2, x and y before cubing

This too. I went the other way because Heidi said she (or he) cubed first, but this is indeed easier.

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