求解 2000(1+.049/12)^12(8)

$$2000 ( 1 + \frac { .049 } { 12 } ) ^ { 12 ( 8 ) }$$

求值

$$\frac{59060404954602459057264725849759706476285134042690263935986471396848028569379477935895578915669838211187195945850276534527494952998493286546705068503277392776088619405722148166341483187610574386546765582800212366398482513158454847095404615855258643381409497096620211250732012633444770889819139622463848039284253443717006823171470117451997971075005778333742306026249669349226174007789312243201}{19969611912136996107833821275978214168984442801260957645259497108971231658230160663526482525483652087808000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}\approx 2957.513907354$$

求解步骤

将分子和分母同时乘以 1000 以展开 \frac{0.049}{12}。

$$2000\left(1+\frac{49}{12000}\right)^{12\times 8}$$

1 与 \frac{49}{12000} 相加，得到 \frac{12049}{12000}。

$$2000\times \left(\frac{12049}{12000}\right)^{12\times 8}$$

将 12 与 8 相乘，得到 96。

$$2000\times \left(\frac{12049}{12000}\right)^{96}$$

计算 96 的 \frac{12049}{12000} 乘方，得到 \frac{59060404954602459057264725849759706476285134042690263935986471396848028569379477935895578915669838211187195945850276534527494952998493286546705068503277392776088619405722148166341483187610574386546765582800212366398482513158454847095404615855258643381409497096620211250732012633444770889819139622463848039284253443717006823171470117451997971075005778333742306026249669349226174007789312243201}{39939223824273992215667642551956428337968885602521915290518994217942463316460321327052965050967304175616000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}。

$$2000\times \frac{59060404954602459057264725849759706476285134042690263935986471396848028569379477935895578915669838211187195945850276534527494952998493286546705068503277392776088619405722148166341483187610574386546765582800212366398482513158454847095404615855258643381409497096620211250732012633444770889819139622463848039284253443717006823171470117451997971075005778333742306026249669349226174007789312243201}{39939223824273992215667642551956428337968885602521915290518994217942463316460321327052965050967304175616000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}$$

将 2000 与 \frac{59060404954602459057264725849759706476285134042690263935986471396848028569379477935895578915669838211187195945850276534527494952998493286546705068503277392776088619405722148166341483187610574386546765582800212366398482513158454847095404615855258643381409497096620211250732012633444770889819139622463848039284253443717006823171470117451997971075005778333742306026249669349226174007789312243201}{39939223824273992215667642551956428337968885602521915290518994217942463316460321327052965050967304175616000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} 相乘，得到 \frac{59060404954602459057264725849759706476285134042690263935986471396848028569379477935895578915669838211187195945850276534527494952998493286546705068503277392776088619405722148166341483187610574386546765582800212366398482513158454847095404615855258643381409497096620211250732012633444770889819139622463848039284253443717006823171470117451997971075005778333742306026249669349226174007789312243201}{19969611912136996107833821275978214168984442801260957645259497108971231658230160663526482525483652087808000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}。

$$\frac{59060404954602459057264725849759706476285134042690263935986471396848028569379477935895578915669838211187195945850276534527494952998493286546705068503277392776088619405722148166341483187610574386546765582800212366398482513158454847095404615855258643381409497096620211250732012633444770889819139622463848039284253443717006823171470117451997971075005778333742306026249669349226174007789312243201}{19969611912136996107833821275978214168984442801260957645259497108971231658230160663526482525483652087808000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}$$

因式分解

$$\frac{12049 ^ {96}}{2 ^ {476} \cdot 3 ^ {96} \cdot 5 ^ {285}} = NaN$$