$\frac{(z x^{-1} y)^5 y^5}{x^{-4} z^{-4}}$
How would I evaluate this if $x = 10$, $y = -3$ and $z = 3$ ? I would like a step-by-step solution to help me fully understand it.
$\frac{(z x^{-1} y)^5 y^5}{x^{-4} z^{-4}}$
How would I evaluate this if $x = 10$, $y = -3$ and $z = 3$ ? I would like a step-by-step solution to help me fully understand it.
You can simply plug in and chug.
Or you can do some algebra first: dividing by $x^{-4}$ is the same as multiplying by $x^4$. Same with $z^{-4}$. So your expression is exactly the same as $ x^4z^4(zx^{-1}y)^5y^5.$ And since $(ab)^n = a^nb^n$, then $(zx^{-1}y)^5 = z^5 (x^{-1})^5 y^5 = z^5 x^{-5}y^5$. So your expression is the same as $x^4 z^4 z^5 x^{-5}y^5y^5.$ Now simplify by putting all the $x$s, all the $y$s and all the $z$s together, plug in the values you have, and perform the operations that are left.
First, use the fact that $x^{-n}=\frac{1}{x^n}$ to find $\frac{(z x^{-1} y)^5 y^5}{x^{-4} z^{-4}}=(zx^{-1}y)^5 \cdot \frac{y^5}{x^{-4}z^{-4}}=\left(\frac{zy}{x}\right)^5\cdot x^4z^4y^5 $ Next, $\left(\frac{zy}{x}\right)^5\cdot x^4z^4y^5=\frac{z^5y^5}{x^5}\cdot x^4z^4y^5=z^9y^{10}x$ Can you finish from here?