解決2000{left(1+0.048/12right)}^12(8) |Microsoft數學求解器

$$2000 { \left(1+ \frac{ 0.048 }{ 12 } \right) }^{ 12(8) }$$

評估

$$2934.042668635337059259811591132969608404278762953177385618816777946166911088994994638032025150363642995124858844856272420646468051230634442907944081674142220918347472493717294034694827869483268890185726068349382395924470013666686269686828021609042609424224292869431641145475635575408033792$$

解題步驟

同時對分子與分母乘上 1000 以展開 \frac{0.048}{12}。

$$2000\left(1+\frac{48}{12000}\right)^{12\times 8}$$

透過找出與消去 48，對分式 \frac{48}{12000} 約分至最低項。

$$2000\left(1+\frac{1}{250}\right)^{12\times 8}$$

將 1 與 \frac{1}{250} 相加可以得到 \frac{251}{250}。

$$2000\times \left(\frac{251}{250}\right)^{12\times 8}$$

將 12 乘上 8 得到 96。

$$2000\times \left(\frac{251}{250}\right)^{96}$$

計算 \frac{251}{250} 的 96 乘冪，然後得到 \frac{233709982116021475511298834435852318285693116072972864647596161757882863903045447037576112472656485331345492451328423481851595726867282650017261507914218447831276989126314709333334293698166302764404836383932921548548197389035024001}{159309191113245227702888039776771180559110455519261878607388585338616290151305816094308987472018268594098344692611135542392730712890625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}。

$$2000\times \frac{233709982116021475511298834435852318285693116072972864647596161757882863903045447037576112472656485331345492451328423481851595726867282650017261507914218447831276989126314709333334293698166302764404836383932921548548197389035024001}{159309191113245227702888039776771180559110455519261878607388585338616290151305816094308987472018268594098344692611135542392730712890625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}$$

將 2000 乘上 \frac{233709982116021475511298834435852318285693116072972864647596161757882863903045447037576112472656485331345492451328423481851595726867282650017261507914218447831276989126314709333334293698166302764404836383932921548548197389035024001}{159309191113245227702888039776771180559110455519261878607388585338616290151305816094308987472018268594098344692611135542392730712890625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} 得到 \frac{233709982116021475511298834435852318285693116072972864647596161757882863903045447037576112472656485331345492451328423481851595726867282650017261507914218447831276989126314709333334293698166302764404836383932921548548197389035024001}{79654595556622613851444019888385590279555227759630939303694292669308145075652908047154493736009134297049172346305567771196365356445312500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}。

$$\frac{233709982116021475511298834435852318285693116072972864647596161757882863903045447037576112472656485331345492451328423481851595726867282650017261507914218447831276989126314709333334293698166302764404836383932921548548197389035024001}{79654595556622613851444019888385590279555227759630939303694292669308145075652908047154493736009134297049172346305567771196365356445312500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}$$

因式分解

$$\frac{251 ^ {96}}{2 ^ {92} \cdot 5 ^ {285}} = 2934\frac{3.398752890732263 \times 10^{225}}{7.965459555662261 \times 10^{226}} = 2934.042668635337$$