(2**5+2**8)**5*2**-5
You asked:
Evaluate the expression: \({\left( {2}^{5} + {2}^{8} \right)}^{5} {2}^{-5}\)
MathBot Answer:
\[{\left( {2}^{5} + {2}^{8} \right)}^{5} {2}^{-5} = 61917364224\]
\[\begin{aligned}{\left( {2}^{5} + {2}^{8} \right)}^{5} {2}^{-5}& = \left(2^{5} + 2^{8}\right)^{5} \cdot \frac{1}{2^{5}}\\& = \left(32 + 2^{8}\right)^{5} \cdot \frac{1}{2^{5}}\\& = \left(32 + 256\right)^{5} \cdot \frac{1}{2^{5}}\\& = 288^{5} \cdot \frac{1}{2^{5}}\\& = 1981355655168 \cdot \frac{1}{2^{5}}\\& = \frac{1981355655168}{32}\\& = 61917364224\end{aligned}\]