Question

Perform the indicated operation.
(9z^3/16xy) * (4x/27z^3)

Answer 1

\((9\cdot \frac{z^3}{16xy})(4\cdot \frac{x}{27z^3})\)?

Answer 2

Assuming the previously mentioned expression:
\[\large{(9\cdot\frac{z^3}{16xy})(4\cdot\frac{x}{27z^3})}\]

Isolate the numerical values.
\[\large{(\frac{9}{16}\cdot\frac{z^3}{xy})(\frac{4}{27}\cdot\frac{x}{z^3})}\]

Find similar terms in numerator and denominator that you can cancel. I crossed them out so you can see.
\[\large{(\frac{9}{16}\cdot\frac{\cancel{z^3}}{\bcancel{x}y})(\frac{4}{27}\cdot\frac{\bcancel{x}}{\cancel{z^3}})}\]

So now you have this left:
\[\large{(\frac{9}{16}\cdot\frac{1}{y})(\frac{4}{27})}\]

Simplify anything you can with the numbers. I rearranged them to show relationships.
\[\large{\frac{9}{27}\cdot\frac{4}{16}\cdot\frac{1}{y}}\rightarrow\frac{1}{3}\cdot\frac{1}{4}\cdot\frac{1}{y}=\frac{1}{12y}\]

And that's your answer.
Sorry if it's weird, I haven't been on here in awhile so I forgot how to use the bracket-type LaTeX formatting.