Question

$$\frac{5\cdot2^{13}\cdot4^{11}-16^{9}}{(3\cdot2^{17})^{2}}$$

Answer

2/3

Solution


Simplify  \({2}^{13}\)  to  \(8192\).
\[\frac{5\times 8192\times {4}^{11}-{16}^{9}}{{(3\times {2}^{17})}^{2}}\]
Simplify  \({4}^{11}\)  to  \(4194304\).
\[\frac{5\times 8192\times 4194304-{16}^{9}}{{(3\times {2}^{17})}^{2}}\]
Simplify  \({16}^{9}\)  to  \(68719476736\).
\[\frac{5\times 8192\times 4194304-68719476736}{{(3\times {2}^{17})}^{2}}\]
Simplify  \(5\times 8192\)  to  \(40960\).
\[\frac{40960\times 4194304-68719476736}{{(3\times {2}^{17})}^{2}}\]
Simplify  \(40960\times 4194304\)  to  \(171798691840\).
\[\frac{171798691840-68719476736}{{(3\times {2}^{17})}^{2}}\]
Simplify  \(171798691840-68719476736\)  to  \(103079215104\).
\[\frac{103079215104}{{(3\times {2}^{17})}^{2}}\]
Simplify  \({2}^{17}\)  to  \(131072\).
\[\frac{103079215104}{{(3\times 131072)}^{2}}\]
Simplify  \(3\times 131072\)  to  \(393216\).
\[\frac{103079215104}{{393216}^{2}}\]
Simplify  \({393216}^{2}\)  to  \(154618822656\).
\[\frac{103079215104}{154618822656}\]
Simplify.
\[\frac{2}{3}\]

Decimal Form: 0.666667