Решете 11-(1/1+15%)^48/15%

$$1 \frac { 1 - ( \frac { 1 } { 1 + 15 \% } ) ^ { 48 } } { 15 \% }$$

Изчисляване

$$\frac{1535728808950087889079913207222960190183200502289339641982122184540}{230640796319223839361986981083444028527480075343400946297318327681}\approx 6,658530639$$

Стъпки на решението

Намаляване на дробта \frac{15}{100} до най-малките членове чрез извличане на корен и съкращаване на 5.

$$1\times \frac{1-\left(\frac{1}{1+\frac{3}{20}}\right)^{48}}{\frac{15}{100}}$$

Съберете 1 и \frac{3}{20}, за да се получи \frac{23}{20}.

$$1\times \frac{1-\left(\frac{1}{\frac{23}{20}}\right)^{48}}{\frac{15}{100}}$$

Разделете 1 на \frac{23}{20} чрез умножаване на 1 по обратната стойност на \frac{23}{20}.

$$1\times \frac{1-\left(1\times \frac{20}{23}\right)^{48}}{\frac{15}{100}}$$

Умножете 1 по \frac{20}{23}, за да получите \frac{20}{23}.

$$1\times \frac{1-\left(\frac{20}{23}\right)^{48}}{\frac{15}{100}}$$

Изчислявате 48 на степен \frac{20}{23} и получавате \frac{281474976710656000000000000000000000000000000000000000000000000}{230640796319223839361986981083444028527480075343400946297318327681}.

$$1\times \frac{1-\frac{281474976710656000000000000000000000000000000000000000000000000}{230640796319223839361986981083444028527480075343400946297318327681}}{\frac{15}{100}}$$

Извадете \frac{281474976710656000000000000000000000000000000000000000000000000}{230640796319223839361986981083444028527480075343400946297318327681} от 1, за да получите \frac{230359321342513183361986981083444028527480075343400946297318327681}{230640796319223839361986981083444028527480075343400946297318327681}.

$$1\times \frac{\frac{230359321342513183361986981083444028527480075343400946297318327681}{230640796319223839361986981083444028527480075343400946297318327681}}{\frac{15}{100}}$$

Намаляване на дробта \frac{15}{100} до най-малките членове чрез извличане на корен и съкращаване на 5.

$$1\times \frac{\frac{230359321342513183361986981083444028527480075343400946297318327681}{230640796319223839361986981083444028527480075343400946297318327681}}{\frac{3}{20}}$$

Разделете \frac{230359321342513183361986981083444028527480075343400946297318327681}{230640796319223839361986981083444028527480075343400946297318327681} на \frac{3}{20} чрез умножаване на \frac{230359321342513183361986981083444028527480075343400946297318327681}{230640796319223839361986981083444028527480075343400946297318327681} по обратната стойност на \frac{3}{20}.

$$1\times \frac{230359321342513183361986981083444028527480075343400946297318327681}{230640796319223839361986981083444028527480075343400946297318327681}\times \frac{20}{3}$$

Умножете \frac{230359321342513183361986981083444028527480075343400946297318327681}{230640796319223839361986981083444028527480075343400946297318327681} по \frac{20}{3}, за да получите \frac{1535728808950087889079913207222960190183200502289339641982122184540}{230640796319223839361986981083444028527480075343400946297318327681}.

$$1\times \frac{1535728808950087889079913207222960190183200502289339641982122184540}{230640796319223839361986981083444028527480075343400946297318327681}$$

Умножете 1 по \frac{1535728808950087889079913207222960190183200502289339641982122184540}{230640796319223839361986981083444028527480075343400946297318327681}, за да получите \frac{1535728808950087889079913207222960190183200502289339641982122184540}{230640796319223839361986981083444028527480075343400946297318327681}.

$$\frac{1535728808950087889079913207222960190183200502289339641982122184540}{230640796319223839361986981083444028527480075343400946297318327681}$$