Question

$$\frac{ { 3 }^{ 2 } }{ \frac{ { 4 }^{ 2 } }{ \frac{ { 9 }^{ 2 } }{ \times 6 } } } =$$

Answer

2187/8

Solution


Simplify  \({9}^{2}\)  to  \(81\).
\[\frac{{3}^{2}}{\frac{{4}^{2}}{\frac{81}{\times 6}}}\]
Use this rule: \(\frac{a}{b} \times c=\frac{ac}{b}\).
\[\frac{{3}^{2}}{\frac{{4}^{2}}{81\times 6}}\]
Simplify  \(81\times 6\)  to  \(486\).
\[\frac{{3}^{2}}{\frac{{4}^{2}}{486}}\]
Simplify  \({4}^{2}\)  to  \(16\).
\[\frac{{3}^{2}}{\frac{16}{486}}\]
Simplify  \(\frac{16}{486}\)  to  \(\frac{8}{243}\).
\[\frac{{3}^{2}}{\frac{8}{243}}\]
Simplify  \({3}^{2}\)  to  \(9\).
\[\frac{9}{\frac{8}{243}}\]
Invert and multiply.
\[9\times \frac{243}{8}\]
Use this rule: \(a \times \frac{b}{c}=\frac{ab}{c}\).
\[\frac{9\times 243}{8}\]
Simplify  \(9\times 243\)  to  \(2187\).
\[\frac{2187}{8}\]

Decimal Form: 273.375