Question

$$( \frac{ 1 }{ 3 } { x }^{ 2 } y)( \frac{ 1 }{ 8 } xy)$$

Answer

$$(x^3*y^2)/24$$

Solution


Simplify  \(\frac{1}{3}{x}^{2}y\)  to  \(\frac{{x}^{2}y}{3}\).
\[\frac{{x}^{2}y}{3}\times \frac{1}{8}xy\]
Simplify.
\[\frac{xy{x}^{2}y}{24}\]
Regroup terms.
\[\frac{x{x}^{2}yy}{24}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\frac{{x}^{1+2}{y}^{1+1}}{24}\]
Simplify  \(1+2\)  to  \(3\).
\[\frac{{x}^{3}{y}^{1+1}}{24}\]
Simplify  \(1+1\)  to  \(2\).
\[\frac{{x}^{3}{y}^{2}}{24}\]