(2^31+2^28)/(2^29+2^26)
You asked:
Evaluate the expression: \(\frac{{2}^{31} + {2}^{28}}{{2}^{29} + {2}^{26}}\)
MathBot Answer:
\[\frac{{2}^{31} + {2}^{28}}{{2}^{29} + {2}^{26}} = 4\]
\[\begin{aligned}\frac{{2}^{31} + {2}^{28}}{{2}^{29} + {2}^{26}}& = \left(2^{31} + 2^{28}\right) \cdot \frac{1}{2^{29} + 2^{26}}\\& = \left(2147483648 + 2^{28}\right) \cdot \frac{1}{2^{29} + 2^{26}}\\& = \left(2147483648 + 268435456\right) \cdot \frac{1}{2^{29} + 2^{26}}\\& = 2415919104 \cdot \frac{1}{2^{29} + 2^{26}}\\& = 2415919104 \cdot \frac{1}{536870912 + 2^{26}}\\& = 2415919104 \cdot \frac{1}{536870912 + 67108864}\\& = \frac{2415919104}{603979776}\\& = 4\end{aligned}\]