simplify the following.
(x^-4*z^7)((2x^{2}y)/(z^-1))^-3

Question

simplify the following.
 (x^-4*z^7)((2x^{2}y)/(z^-1))^-3

anonymous · Answer

Err
$$(x^{-4}z^7)[{(2x^{2}y)\over(z^{-1})}]^{-3}$$
This?

anonymous · Answer

$$ (x^{-4}*z^7)({\frac{2x^{2}y}{z^-1}})^{-3}$$

anonymous · Answer

Yeah, so what I wrote.

anonymous · Answer

yeah.
z to the -1. z^(-1)

anonymous · Answer

So start by distributing the -3 exponent to the numerator & denominator.

anonymous · Answer

i got that. down.
i have 
$$(x^{-4})\frac{z^3}{8x^6y^3}$$

anonymous · Answer

oops i mean. (x^-4*z^7)

anonymous · Answer

Good! Now combine the two factors

anonymous · Answer

Into one fractional expression I mean

anonymous · Answer

do i just multiply the (x^-4*z^7) by the numerator and that's all?

anonymous · Answer

And simplify, yes.

anonymous · Answer

ok so i got. 
$$\frac{z^{21}}{8xz^{12}x^6y^3}$$

anonymous · Answer

That's not right. I'm not sure how you got that actually? Can you explain?

anonymous · Answer

oops i messed up. should have added the exponents not multiplied. i see my mistake.

anonymous · Answer

When you multiply powers of the same base you do add their exponents.

anonymous · Answer

yeah i figured. thanks. appreciate it.