I can't figure out how to simplify this exponent!!

Hi everyone!

I'm new to this forum, so I may not be doing something right, but I just couldn't figure out how to do this problem! I would really like to know **how** to do it and the answer.

__(2*x^2*y^3)*(2*x^4*y^5)^3__

4*x^-3*y^6

Thank you for any much needed help!

Re: I can't figure out how to simplify this exponent!!

Hey Somerset.

For this problem, can you collect all the x powers and y powers together and simplify?

Remember that a^x * a^y = a^(x+y) and a^x / a^y = a^(x-y).

Re: I can't figure out how to simplify this exponent!!

Hi Chiro!

So would I be right to say that the lowest it can go is:

4*x^18*y^9?

Re: I can't figure out how to simplify this exponent!!

Quote:

Originally Posted by

**Somerset** __(2*x^2*y^3)*(2*x^4*y^5)^3__

4*x^-3*y^6

Check your powers again.

$\displaystyle \frac{(2*x^2*y^3)*(2*x^4*y^5)^3}{4*x^{-3}*y^6}$

$\displaystyle = \frac{2 \cdot 2^3}{4} \cdot \frac{x^2 \cdot \left ( x^4 \right )^3}{x^{-3}} \cdot \frac{y^3 \cdot \left ( y^5 \right ) ^3}{y^6}$

Just as a thought, one of the exponent rules is $\displaystyle \left ( x^a \right ) ^b = x^{ab}$.

-Dan

Re: I can't figure out how to simplify this exponent!!

Good day topsquark,

The way you laid that out makes it much easier to see!

So it would then be this correct? I may be way out of the ball park here.

4*x^18*y^12

Thanks!

Re: I can't figure out how to simplify this exponent!!

Quote:

Originally Posted by

**Somerset** Good day topsquark,

The way you laid that out makes it much easier to see!

So it would then be this correct? I may be way out of the ball park here.

4*x^18*y^12

Thanks!

You're still off on the x, but you got the y.

$\displaystyle \frac{x^2 \cdot \left ( x^4 \right ) ^3}{x^{-3}} = \frac{x^2 \cdot x^{4*3}}{x^{-3}}$

$\displaystyle = \frac{x^2 \cdot x^{12}}{x^{-3}} = \frac{x^{2 + 12}}{x^{-3}} = \frac{x^{14}}{x^{-3}}$

Now, to clear the fraction out we have the rule $\displaystyle a^{-b} = \frac{1}{a^b}$ and $\displaystyle \frac{1}{a^{-b}} = a^b$.

$\displaystyle \frac{x^{14}}{x^{-3}} = x^{14} \cdot x^3 = x^{17}$

-Dan

Re: I can't figure out how to simplify this exponent!!

Oh! I messed up my math there!

Thank you so much for your help!