Solve 40div00585*(1-10585^-16+1000div10585^16

$$40 \div 00585 \times (1- { 10585 }^{ -16 } +1000 \div { 10585 }^{ 16 }$$

Evaluate

$$\frac{198675257548959465311315767701635536295755262480851173095703132992}{2905625641653532180177993102636419718325420713782448406524658203125}\approx 0.068376068$$

Solution Steps

Reduce the fraction \frac{40}{585} to lowest terms by extracting and canceling out 5.

$$\frac{8}{117}\left(1-10585^{-16}+\frac{1000}{10585^{16}}\right)$$

Calculate 10585 to the power of -16 and get \frac{1}{24834407193619933163914470962704442036969407810106396636962890625}.

$$\frac{8}{117}\left(1-\frac{1}{24834407193619933163914470962704442036969407810106396636962890625}+\frac{1000}{10585^{16}}\right)$$

Subtract \frac{1}{24834407193619933163914470962704442036969407810106396636962890625} from 1 to get \frac{24834407193619933163914470962704442036969407810106396636962890624}{24834407193619933163914470962704442036969407810106396636962890625}.

$$\frac{8}{117}\left(\frac{24834407193619933163914470962704442036969407810106396636962890624}{24834407193619933163914470962704442036969407810106396636962890625}+\frac{1000}{10585^{16}}\right)$$

Calculate 10585 to the power of 16 and get 24834407193619933163914470962704442036969407810106396636962890625.

$$\frac{8}{117}\left(\frac{24834407193619933163914470962704442036969407810106396636962890624}{24834407193619933163914470962704442036969407810106396636962890625}+\frac{1000}{24834407193619933163914470962704442036969407810106396636962890625}\right)$$

Reduce the fraction \frac{1000}{24834407193619933163914470962704442036969407810106396636962890625} to lowest terms by extracting and canceling out 125.

$$\frac{8}{117}\left(\frac{24834407193619933163914470962704442036969407810106396636962890624}{24834407193619933163914470962704442036969407810106396636962890625}+\frac{8}{198675257548959465311315767701635536295755262480851173095703125}\right)$$

Add \frac{24834407193619933163914470962704442036969407810106396636962890624}{24834407193619933163914470962704442036969407810106396636962890625} and \frac{8}{198675257548959465311315767701635536295755262480851173095703125} to get \frac{24834407193619933163914470962704442036969407810106396636962891624}{24834407193619933163914470962704442036969407810106396636962890625}.

$$\frac{8}{117}\times \frac{24834407193619933163914470962704442036969407810106396636962891624}{24834407193619933163914470962704442036969407810106396636962890625}$$

Multiply \frac{8}{117} and \frac{24834407193619933163914470962704442036969407810106396636962891624}{24834407193619933163914470962704442036969407810106396636962890625} to get \frac{198675257548959465311315767701635536295755262480851173095703132992}{2905625641653532180177993102636419718325420713782448406524658203125}.

$$\frac{198675257548959465311315767701635536295755262480851173095703132992}{2905625641653532180177993102636419718325420713782448406524658203125}$$