4 /(216)^ -2÷3 + 1/(256)^ -3÷4 + 2/(243) ^ -1÷5

asked by guest
on Jan 07, 2025 at 6:45 am



You asked:

Evaluate the expression: \(\frac{\frac{4}{{216}^{-2}}}{3} + \frac{\frac{1}{{256}^{-3}}}{4} + \frac{\frac{2}{{243}^{-1}}}{5}\)

MathBot Answer:

\[\frac{\frac{4}{{216}^{-2}}}{3} + \frac{\frac{1}{{256}^{-3}}}{4} + \frac{\frac{2}{{243}^{-1}}}{5} = \frac{21283046}{5} = 4256609.2\]

\[\begin{aligned}\frac{\frac{4}{{216}^{-2}}}{3} + \frac{\frac{1}{{256}^{-3}}}{4} + \frac{\frac{2}{{243}^{-1}}}{5}&=\frac{\frac{4}{\frac{1}{46656}}}{3} + \frac{\frac{1}{{256}^{-3}}}{4} + \frac{\frac{2}{{243}^{-1}}}{5}\\&=\frac{186624}{3} + \frac{\frac{1}{{256}^{-3}}}{4} + \frac{\frac{2}{{243}^{-1}}}{5}\\&=62208 + \frac{\frac{1}{{256}^{-3}}}{4} + \frac{\frac{2}{{243}^{-1}}}{5}\\&=62208 + \frac{\frac{1}{\frac{1}{16777216}}}{4} + \frac{\frac{2}{{243}^{-1}}}{5}\\&=62208 + \frac{16777216}{4} + \frac{\frac{2}{{243}^{-1}}}{5}\\&=62208 + 4194304 + \frac{\frac{2}{{243}^{-1}}}{5}\\&=4256512 + \frac{\frac{2}{{243}^{-1}}}{5}\\&=4256512 + \frac{\frac{2}{\frac{1}{243}}}{5}\\&=4256512 + \frac{486}{5}\\&=\frac{21283046}{5}\end{aligned}\]

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