1. ## Multiplying/dividing with exponents

I am having difficulties figuring out what exactly the author of my Algebra book is doing in regards to step 2.

Expression
$(\frac{x^3}{y^2}^5) (\frac{x}{y})^{-2}$

Step 1= $\frac{x^{15}}{y^{10}} * \frac{y^2}{x^2}$

Step 2= $x^{15-2} y^{2-10}$

Could some one please clearly explain whats going on from step 1 to step 2. When the expression turns into $x^{15-2} y^{2-10}$ is where im the most confused, if someone would please explain this transition that would be greatly appreciated. Unless the author is using $\frac{a^m}{a^n}=a^{n*m}$ to combine BOTH fractions.

Thanks!

2. Originally Posted by allyourbass2212
I am having difficulties figuring out what exactly the author of my Algebra book is doing in regards to step 2.

Expression
$(\frac{x^3}{y^2}^5) (\frac{x}{y})^{-2}$

Step 1= $\frac{x^{15}}{y^{10}} * \frac{y^2}{x^2}$

Step 2= $x^{15-2} y^{2-10}$

Could some one please clearly explain whats going on from step 1 to step 2. When the expression turns into $x^{15-2} y^{2-10}$ is where im the most confused, if someone would please explain this transition that would be greatly appreciated. Unless the author is using $\frac{a^m}{a^n}=a^{n*m}$ to combine BOTH fractions.

Thanks!
Look for exponent laws:
Exponent Laws - Learning Algebra Fundamentals

press the green button every time.

3. Yes I understand when its a single fraction using $\frac{a^m}{a^n}=a^{m-n}$. I am familiar with the exponent laws and in fact I have them laying out in front of me. I am just uncertain whats going on in this particular situation.

4. I am no math expert, but I think this might help clarify.

Instead of seeing it like this
$\frac{x^{15}}{y^{10}} * \frac{y^2}{x^2}$

View it as this
$\frac{x^{15}y^2}{y^{10}x^2}$

Then just use the exponent property
$\frac{a^m}{a^n}=a^{m-n}$ to solve the rest.

e.g.

15-2, 2-10 resulting in $x^{13}y^{-8}$
or $\frac{x^{13}}{y^8}$ if you want to remove negative exponents using the property $a^{-n}=\frac{1}{a^n}$

But again im no expert at math, I would have someone else verify this statement. I would hate to be the source of any confusion.

5. Originally Posted by allyourbass2212
Yes I understand when its a single fraction using $\frac{a^m}{a^n}=a^{m-n}$. I am familiar with the exponent laws and in fact I have them laying out in front of me. I am just uncertain whats going on in this particular situation.
$
\frac{x^{15}}{y^{10}} \;\times\;\frac{y^2}{x^2}$

$
\frac{x^{15}}{x^2}\;\times\;\frac{y^2}{y^{10}}
$

$
x^{15-2}\;\times \;y^{2-10}
$

$
x^{13}\;\times \;y^{-8}
$

$
x^{13}\;\times \;\frac{1}{y^{8}}
$

$
\frac{x^{13}}{y^{8}}
$

6. Thanks both of you.

I think the way cmf0106 set it up is easier to understand though... can anyone confirm he did it correctly?

Thanks again guys.

7. Originally Posted by allyourbass2212
Thanks both of you.

I think the way cmf0106 set it up is easier to understand though... can anyone confirm he did it correctly?

Thanks again guys.
yes, he did correctly.