解決{left(2.036/2right)}^40*6500 |Microsoft數學求解器

$${ \left( \frac{ 2.036 }{ 2 } \right) }^{ 40 } \times 6500$$

評估

$$13268.580898360985919961236104895274231728861081353902675408925321643929236720131091884645068094188325016410945801571794944$$

解題步驟

同時對分子與分母乘上 1000 以展開 \frac{2.036}{2}。

$$\left(\frac{2036}{2000}\right)^{40}\times 6500$$

透過找出與消去 4，對分式 \frac{2036}{2000} 約分至最低項。

$$\left(\frac{509}{500}\right)^{40}\times 6500$$

計算 \frac{509}{500} 的 40 乘冪，然後得到 \frac{1856569850323814943499024188530959653442111711628114744656078608336629151901732130036130361160224846084077601}{909494701772928237915039062500000000000000000000000000000000000000000000000000000000000000000000000000000000}。

$$\frac{1856569850323814943499024188530959653442111711628114744656078608336629151901732130036130361160224846084077601}{909494701772928237915039062500000000000000000000000000000000000000000000000000000000000000000000000000000000}\times 6500$$

將 \frac{1856569850323814943499024188530959653442111711628114744656078608336629151901732130036130361160224846084077601}{909494701772928237915039062500000000000000000000000000000000000000000000000000000000000000000000000000000000} 乘上 6500 得到 \frac{24135408054209594265487314450902475494747452251165491680529021908376178974722517690469694695082922999093008813}{1818989403545856475830078125000000000000000000000000000000000000000000000000000000000000000000000000000000}。

$$\frac{24135408054209594265487314450902475494747452251165491680529021908376178974722517690469694695082922999093008813}{1818989403545856475830078125000000000000000000000000000000000000000000000000000000000000000000000000000000}$$

因式分解

$$\frac{13 \cdot 509 ^ {40}}{2 ^ {78} \cdot 5 ^ {117}} = 13268\frac{1.0566479631706938 \times 10^{105}}{1.8189894035458567 \times 10^{105}} = 13268.580898360986$$