# Thread: Simplifying fractions with exponents

1. ## Simplifying fractions with exponents

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

2. Originally Posted by HeidiHectic
I have to simplify this and im totally confused step by step help would be so much appreciated!
$\displaystyle \left( \frac {-6x^2y}{2xy^3} \right)^3$
Have you made any attempt at the problem? You should be familiar with these properties of exponentiation:

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

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

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

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

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

(where $\displaystyle a,\,b,\,m$ and $\displaystyle n$ 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.

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

4. Originally Posted by HeidiHectic
yes, i understand those im just not sure what to do after you distribute the exponent.
$\displaystyle \left(\frac{-6x^2y}{2xy^3}\right)^3$

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

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

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

Now can you see how to continue?

5. Originally Posted by HeidiHectic
I have to simplify this and im totally confused step by step help would be so much appreciated!
$\displaystyle \left( \frac {-6x^2y}{2xy^3} \right)^3$
I'd cancel a factor of 2, x and y before cubing

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

6. 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.

### heidihectic

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