Solve 160,000(1-45/12)^120

$$160,000 ( 1 - \frac { 45 } { 12 } ) ^ { 120 }$$

Evaluate

$$\frac{57943168011143788736575379058871153662317125935685648593652986267390060901342479354660849399055525836253753770370371493534500625}{6901746346790563787434755862277025452451108972170386555162524223799296}\approx 8.395435749 \cdot 10^{57}$$

Solution Steps

Reduce the fraction \frac{45}{12} to lowest terms by extracting and canceling out 3.

$$160000\left(1-\frac{15}{4}\right)^{120}$$

Subtract \frac{15}{4} from 1 to get -\frac{11}{4}.

$$160000\left(-\frac{11}{4}\right)^{120}$$

Calculate -\frac{11}{4} to the power of 120 and get \frac{92709068817830061978520606494193845859707401497097037749844778027824097442147966967457359038488841338006006032592594389655201}{1766847064778384329583297500742918515827483896875618958121606201292619776}.

$$160000\times \frac{92709068817830061978520606494193845859707401497097037749844778027824097442147966967457359038488841338006006032592594389655201}{1766847064778384329583297500742918515827483896875618958121606201292619776}$$

Multiply 160000 and \frac{92709068817830061978520606494193845859707401497097037749844778027824097442147966967457359038488841338006006032592594389655201}{1766847064778384329583297500742918515827483896875618958121606201292619776} to get \frac{57943168011143788736575379058871153662317125935685648593652986267390060901342479354660849399055525836253753770370371493534500625}{6901746346790563787434755862277025452451108972170386555162524223799296}.

$$\frac{57943168011143788736575379058871153662317125935685648593652986267390060901342479354660849399055525836253753770370371493534500625}{6901746346790563787434755862277025452451108972170386555162524223799296}$$

Factor

$$\frac{5 ^ {4} \cdot 11 ^ {120}}{2 ^ {232}} = 8.395435749111297 \times 10^{57}$$