Question

$$\frac{ 88888 }{ \frac{ 99999 }{ \frac{ 99999 }{ \frac{ 44444 }{ \frac{ 55555 }{ 6666- } } } } }$$

Answer

$$(4.9381234582716*10^14)/(2.9626074136296*10^13-)$$

Solution


Invert and multiply.
\[\frac{88888}{\frac{99999}{\frac{99999}{44444\times \frac{6666-}{55555}}}}\]
Use this rule: \(a \times \frac{b}{c}=\frac{ab}{c}\).
\[\frac{88888}{\frac{99999}{\frac{99999}{\frac{44444\times 6666-}{55555}}}}\]
Simplify  \(44444\times 6666\)  to  \(296263704\).
\[\frac{88888}{\frac{99999}{\frac{99999}{\frac{296263704-}{55555}}}}\]
Invert and multiply.
\[\frac{88888}{\frac{99999}{99999\times \frac{55555}{296263704-}}}\]
Use this rule: \(a \times \frac{b}{c}=\frac{ab}{c}\).
\[\frac{88888}{\frac{99999}{\frac{99999\times 55555}{296263704-}}}\]
Simplify  \(99999\times 55555\)  to  \(5555444445\).
\[\frac{88888}{\frac{99999}{\frac{5555444445}{296263704-}}}\]
Invert and multiply.
\[\frac{88888}{99999\times \frac{296263704-}{5555444445}}\]
Use this rule: \(a \times \frac{b}{c}=\frac{ab}{c}\).
\[\frac{88888}{\frac{99999\times 296263704-}{5555444445}}\]
Simplify  \(99999\times 296263704\)  to  \(2.962607\times {10}^{13}\).
\[\frac{88888}{\frac{2.962607\times {10}^{13}-}{5555444445}}\]
Invert and multiply.
\[88888\times \frac{5555444445}{2.962607\times {10}^{13}-}\]
Use this rule: \(a \times \frac{b}{c}=\frac{ab}{c}\).
\[\frac{88888\times 5555444445}{2.962607\times {10}^{13}-}\]
Simplify  \(88888\times 5555444445\)  to  \(4.938123\times {10}^{14}\).
\[\frac{4.938123\times {10}^{14}}{2.962607\times {10}^{13}-}\]