# Math Help - How to simplify this?

1. ## How to simplify this?

Hi there, havn't done math in a while and I switched back to an advanced course so im a little behind.

The question asks me to simplify $\frac{(3x^{4}y^{5}z^{7})^{5}}{(-3x^{3}yz^{4})^{7}}$

I get this: $\frac{3^{5}x^{9}y^{10}z^{12}}{-3^{7}x^{10}y^{7}z^{11}}$ = $-3^{-2}x^{-1}y^{3}z^{1}$=$\frac{1}{-3^{2}} \frac{1}{x} y^{3}z^{1}$

It just doesn't feel right though, can you show me where I went wrong?

2. ## Re: How to simplify this?

$(x^a)^b = x^{ab}$ NOT $x^{a+b}$ as you've done.

$\dfrac{(3x^4 y^5 z^7)^5}{(-3x^3 y z^4)^7}=$

$\dfrac {3^5 x^{20} y^{25} z^{35}}{(-3)^7 x^{21} y^7 z^{28}}=$

$\dfrac {3^5 y^{18} z^7}{(-1)^7 (3)^7 x} =$

$-\dfrac{y^{18}z^7}{9x}$

3. ## Re: How to simplify this?

thank you for clearing that up