Question

$$\frac{ 8 }{ \frac{ 9 }{ \frac{ 9 }{ 6 \times } \times } \times } \times$$

Answer

$$8/(6*^2)$$

Solution


Use this rule: \(\frac{a}{b} \times c=\frac{ac}{b}\).
\[\frac{8}{\frac{9}{\frac{9}{6}}}\]
Simplify  \(\frac{9}{6}\)  to  \(\frac{9}{6}\).
\[\frac{8}{\frac{9}{\frac{9}{6}}}\]
Simplify  \(\frac{9}{6}\)  to  \(\frac{3}{2}\).
\[\frac{8}{\frac{9}{\frac{3}{2}}}\]
Invert and multiply.
\[\frac{8}{(9\times \frac{2}{3})}\]
Use this rule: \(a \times \frac{b}{c}=\frac{ab}{c}\).
\[\frac{8}{\frac{9\times 2}{3}}\]
Simplify  \(9\times 2\)  to  \(18\).
\[\frac{8}{\frac{18}{3}}\]
Simplify  \(\frac{18}{3}\)  to  \(6\).
\[\frac{8}{6}\]
Simplify.
\[\frac{8}{6{}^{2}}\]