Question

$$3/4/ \frac{ 9 \times }{ 6 \times } \frac{ 1 }{ 6 }$$

Answer

$$3/(1296*^2)$$

Solution


Simplify  \(\frac{\frac{\frac{3}{4}}{9}}{6}\)  to  \(\frac{3}{4\times 9\times 6}\).
\[\frac{3}{4\times 9\times 6}\times \frac{1}{6}\]
Simplify  \(4\times 9\)  to  \(36\).
\[\frac{3}{36\times 6}\times \frac{1}{6}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\frac{3}{36{}^{2}\times 6}\times \frac{1}{6}\]
Simplify  \(36{}^{2}\times 6\)  to  \(216{}^{2}\).
\[\frac{3}{216{}^{2}}\times \frac{1}{6}\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{3\times 1}{216{}^{2}\times 6}\]
Simplify  \(3\times 1\)  to  \(3\).
\[\frac{3}{216{}^{2}\times 6}\]
Simplify  \(216{}^{2}\times 6\)  to  \(1296{}^{2}\).
\[\frac{3}{1296{}^{2}}\]