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

1. ## 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!

2. ## 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).

3. ## 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?

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

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

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

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

-Dan

5. ## 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!

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

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

7. ## 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!