2^30+4^20/4^30-2^20

asked by guest
on Oct 22, 2024 at 11:15 pm



You asked:

Evaluate the expression: \({2}^{30} + \frac{{4}^{20}}{{4}^{30}} - {2}^{20}\)

MathBot Answer:

\[{2}^{30} + \frac{{4}^{20}}{{4}^{30}} - {2}^{20} = \frac{1124800395214849}{1048576} = 1072693248.00000095367431640625\]

\[\begin{aligned}{2}^{30} + \frac{{4}^{20}}{{4}^{30}} - {2}^{20}& = 2^{30} + 4^{20} \cdot \frac{1}{4^{30}} - 2^{20}\\& = 1073741824 + 4^{20} \cdot \frac{1}{4^{30}} - 2^{20}\\& = 1073741824 + 1099511627776 \cdot \frac{1}{4^{30}} - 2^{20}\\& = 1073741824 + \frac{1099511627776}{1152921504606846976} - 2^{20}\\& = 1073741824 + \frac{1}{1048576} - 2^{20}\\& = 1073741824 + \frac{1}{1048576} - 1048576\\& = \frac{1125899906842625}{1048576} - 1048576\\& = \frac{1124800395214849}{1048576}\end{aligned}\]

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