Lutasin ang 11-(1/1+15%)^48/15%

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

I-evaluate

$$\frac{1535728808950087889079913207222960190183200502289339641982122184540}{230640796319223839361986981083444028527480075343400946297318327681}\approx 6.658530639$$

Mga Hakbang ng Solution

Bawasan ang fraction \frac{15}{100} sa pinakamabababang term sa pamamagitan ng pag-extract at pag-cancel out sa 5.

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

Idagdag ang 1 at \frac{3}{20} para makuha ang \frac{23}{20}.

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

I-divide ang 1 gamit ang \frac{23}{20} sa pamamagitan ng pagmu-multiply sa 1 gamit ang reciprocal ng \frac{23}{20}.

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

I-multiply ang 1 at \frac{20}{23} para makuha ang \frac{20}{23}.

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

Kalkulahin ang \frac{20}{23} sa power ng 48 at kunin ang \frac{281474976710656000000000000000000000000000000000000000000000000}{230640796319223839361986981083444028527480075343400946297318327681}.

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

I-subtract ang \frac{281474976710656000000000000000000000000000000000000000000000000}{230640796319223839361986981083444028527480075343400946297318327681} mula sa 1 para makuha ang \frac{230359321342513183361986981083444028527480075343400946297318327681}{230640796319223839361986981083444028527480075343400946297318327681}.

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

Bawasan ang fraction \frac{15}{100} sa pinakamabababang term sa pamamagitan ng pag-extract at pag-cancel out sa 5.

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

I-divide ang \frac{230359321342513183361986981083444028527480075343400946297318327681}{230640796319223839361986981083444028527480075343400946297318327681} gamit ang \frac{3}{20} sa pamamagitan ng pagmu-multiply sa \frac{230359321342513183361986981083444028527480075343400946297318327681}{230640796319223839361986981083444028527480075343400946297318327681} gamit ang reciprocal ng \frac{3}{20}.

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

I-multiply ang \frac{230359321342513183361986981083444028527480075343400946297318327681}{230640796319223839361986981083444028527480075343400946297318327681} at \frac{20}{3} para makuha ang \frac{1535728808950087889079913207222960190183200502289339641982122184540}{230640796319223839361986981083444028527480075343400946297318327681}.

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

I-multiply ang 1 at \frac{1535728808950087889079913207222960190183200502289339641982122184540}{230640796319223839361986981083444028527480075343400946297318327681} para makuha ang \frac{1535728808950087889079913207222960190183200502289339641982122184540}{230640796319223839361986981083444028527480075343400946297318327681}.

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