Solve 1-(1+8%)^-10/8%

$$\frac { 1 - ( 1 + 8 \% ) ^ { - 10 } } { 8 \% }$$

Evaluate

$$\frac{1381546255675300}{205891132094649}\approx 6.710081399$$

Solution Steps

Reduce the fraction \frac{8}{100} to lowest terms by extracting and canceling out 4.

$$\frac{1-\left(1+\frac{2}{25}\right)^{-10}}{\frac{8}{100}}$$

Add 1 and \frac{2}{25} to get \frac{27}{25}.

$$\frac{1-\left(\frac{27}{25}\right)^{-10}}{\frac{8}{100}}$$

Calculate \frac{27}{25} to the power of -10 and get \frac{95367431640625}{205891132094649}.

$$\frac{1-\frac{95367431640625}{205891132094649}}{\frac{8}{100}}$$

Subtract \frac{95367431640625}{205891132094649} from 1 to get \frac{110523700454024}{205891132094649}.

$$\frac{\frac{110523700454024}{205891132094649}}{\frac{8}{100}}$$

Reduce the fraction \frac{8}{100} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{110523700454024}{205891132094649}}{\frac{2}{25}}$$

Divide \frac{110523700454024}{205891132094649} by \frac{2}{25} by multiplying \frac{110523700454024}{205891132094649} by the reciprocal of \frac{2}{25}.

$$\frac{110523700454024}{205891132094649}\times \frac{25}{2}$$

Multiply \frac{110523700454024}{205891132094649} and \frac{25}{2} to get \frac{1381546255675300}{205891132094649}.

$$\frac{1381546255675300}{205891132094649}$$

Factor

$$\frac{2 ^ {2} \cdot 5 ^ {2} \cdot 11 \cdot 13 \cdot 181 \cdot 1151 \cdot 463741}{3 ^ {30}} = 6\frac{146199463107406}{205891132094649} = 6.710081398941444$$