Question

$$\frac{ { 3 }^{ 2 } }{ \frac{ { 5 }^{ 2 } }{ \frac{ { 8 }^{ 2 } }{ \times { 6 }^{ 2 } } } }$$

Answer

20736/25

Solution


Simplify  \({8}^{2}\)  to  \(64\).
\[\frac{{3}^{2}}{\frac{{5}^{2}}{\frac{64}{\times {6}^{2}}}}\]
Simplify  \({6}^{2}\)  to  \(36\).
\[\frac{{3}^{2}}{\frac{{5}^{2}}{\frac{64}{\times 36}}}\]
Use this rule: \(\frac{a}{b} \times c=\frac{ac}{b}\).
\[\frac{{3}^{2}}{\frac{{5}^{2}}{64\times 36}}\]
Simplify  \(64\times 36\)  to  \(2304\).
\[\frac{{3}^{2}}{\frac{{5}^{2}}{2304}}\]
Simplify  \({5}^{2}\)  to  \(25\).
\[\frac{{3}^{2}}{\frac{25}{2304}}\]
Simplify  \({3}^{2}\)  to  \(9\).
\[\frac{9}{\frac{25}{2304}}\]
Invert and multiply.
\[9\times \frac{2304}{25}\]
Use this rule: \(a \times \frac{b}{c}=\frac{ab}{c}\).
\[\frac{9\times 2304}{25}\]
Simplify  \(9\times 2304\)  to  \(20736\).
\[\frac{20736}{25}\]

Decimal Form: 829.44