Resol [(2-13/5)^2+(5/8-3/4)-(6/5*frac{1}{3})^4*(7frac{1}{2})^3]:(5-frac{6}{5})

$$[ ( 2 - 1 \frac { 3 } { 5 } ) ^ { 2 } + ( \frac { 5 } { 8 } - \frac { 3 } { 4 } ) - ( \frac { 6 } { 5 } \cdot \frac { 1 } { 3 } ) ^ { 4 } \cdot ( 7 \frac { 1 } { 2 } ) ^ { 3 } ] : ( 5 - \frac { 6 } { 5 } )$$

Calcula

$$-\frac{2153}{760}\approx -2,832894737$$

Passos de solució

Multipliqueu 1 per 5 per obtenir 5.

$$\frac{\left(2-\frac{5+3}{5}\right)^{2}+\frac{5}{8}-\frac{3}{4}-\left(\frac{6}{5}\times \frac{1}{3}\right)^{4}\times \left(\frac{7\times 2+1}{2}\right)^{3}}{5-\frac{6}{5}}$$

Sumeu 5 més 3 per obtenir 8.

$$\frac{\left(2-\frac{8}{5}\right)^{2}+\frac{5}{8}-\frac{3}{4}-\left(\frac{6}{5}\times \frac{1}{3}\right)^{4}\times \left(\frac{7\times 2+1}{2}\right)^{3}}{5-\frac{6}{5}}$$

Resteu 2 de \frac{8}{5} per obtenir \frac{2}{5}.

$$\frac{\left(\frac{2}{5}\right)^{2}+\frac{5}{8}-\frac{3}{4}-\left(\frac{6}{5}\times \frac{1}{3}\right)^{4}\times \left(\frac{7\times 2+1}{2}\right)^{3}}{5-\frac{6}{5}}$$

Calculeu \frac{2}{5} elevat a 2 per obtenir \frac{4}{25}.

$$\frac{\frac{4}{25}+\frac{5}{8}-\frac{3}{4}-\left(\frac{6}{5}\times \frac{1}{3}\right)^{4}\times \left(\frac{7\times 2+1}{2}\right)^{3}}{5-\frac{6}{5}}$$

Sumeu \frac{4}{25} més \frac{5}{8} per obtenir \frac{157}{200}.

$$\frac{\frac{157}{200}-\frac{3}{4}-\left(\frac{6}{5}\times \frac{1}{3}\right)^{4}\times \left(\frac{7\times 2+1}{2}\right)^{3}}{5-\frac{6}{5}}$$

Resteu \frac{157}{200} de \frac{3}{4} per obtenir \frac{7}{200}.

$$\frac{\frac{7}{200}-\left(\frac{6}{5}\times \frac{1}{3}\right)^{4}\times \left(\frac{7\times 2+1}{2}\right)^{3}}{5-\frac{6}{5}}$$

Multipliqueu \frac{6}{5} per \frac{1}{3} per obtenir \frac{2}{5}.

$$\frac{\frac{7}{200}-\left(\frac{2}{5}\right)^{4}\times \left(\frac{7\times 2+1}{2}\right)^{3}}{5-\frac{6}{5}}$$

Calculeu \frac{2}{5} elevat a 4 per obtenir \frac{16}{625}.

$$\frac{\frac{7}{200}-\frac{16}{625}\times \left(\frac{7\times 2+1}{2}\right)^{3}}{5-\frac{6}{5}}$$

Multipliqueu 7 per 2 per obtenir 14.

$$\frac{\frac{7}{200}-\frac{16}{625}\times \left(\frac{14+1}{2}\right)^{3}}{5-\frac{6}{5}}$$

Sumeu 14 més 1 per obtenir 15.

$$\frac{\frac{7}{200}-\frac{16}{625}\times \left(\frac{15}{2}\right)^{3}}{5-\frac{6}{5}}$$

Calculeu \frac{15}{2} elevat a 3 per obtenir \frac{3375}{8}.

$$\frac{\frac{7}{200}-\frac{16}{625}\times \frac{3375}{8}}{5-\frac{6}{5}}$$

Multipliqueu \frac{16}{625} per \frac{3375}{8} per obtenir \frac{54}{5}.

$$\frac{\frac{7}{200}-\frac{54}{5}}{5-\frac{6}{5}}$$

Resteu \frac{7}{200} de \frac{54}{5} per obtenir -\frac{2153}{200}.

$$\frac{-\frac{2153}{200}}{5-\frac{6}{5}}$$

Resteu 5 de \frac{6}{5} per obtenir \frac{19}{5}.

$$\frac{-\frac{2153}{200}}{\frac{19}{5}}$$

Dividiu -\frac{2153}{200} per \frac{19}{5} multiplicant -\frac{2153}{200} pel recíproc de \frac{19}{5}.

$$-\frac{2153}{200}\times \frac{5}{19}$$

Multipliqueu -\frac{2153}{200} per \frac{5}{19} per obtenir -\frac{2153}{760}.

$$-\frac{2153}{760}$$

Factoritzar

$$-\frac{2153}{760} = -2\frac{633}{760} = -2,832894736842105$$