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

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

Luacháil

$$-\frac{2153}{760}\approx -2.832894737$$

Céimeanna Réitigh

Méadaigh 1 agus 5 chun 5 a fháil.

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

Suimigh 5 agus 3 chun 8 a fháil.

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

Dealaigh \frac{8}{5} ó 2 chun \frac{2}{5} a fháil.

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

Ríomh cumhacht \frac{2}{5} de 2 agus faigh \frac{4}{25}.

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

Suimigh \frac{4}{25} agus \frac{5}{8} chun \frac{157}{200} a fháil.

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

Dealaigh \frac{3}{4} ó \frac{157}{200} chun \frac{7}{200} a fháil.

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

Méadaigh \frac{6}{5} agus \frac{1}{3} chun \frac{2}{5} a fháil.

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

Ríomh cumhacht \frac{2}{5} de 4 agus faigh \frac{16}{625}.

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

Méadaigh 7 agus 2 chun 14 a fháil.

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

Suimigh 14 agus 1 chun 15 a fháil.

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

Ríomh cumhacht \frac{15}{2} de 3 agus faigh \frac{3375}{8}.

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

Méadaigh \frac{16}{625} agus \frac{3375}{8} chun \frac{54}{5} a fháil.

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

Dealaigh \frac{54}{5} ó \frac{7}{200} chun -\frac{2153}{200} a fháil.

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

Dealaigh \frac{6}{5} ó 5 chun \frac{19}{5} a fháil.

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

Roinn -\frac{2153}{200} faoi \frac{19}{5} trí -\frac{2153}{200} a mhéadú faoi dheilín \frac{19}{5}.

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

Méadaigh -\frac{2153}{200} agus \frac{5}{19} chun -\frac{2153}{760} a fháil.

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

Fachtóirigh

$$-\frac{2153}{760} = -2\frac{633}{760} = -2.832894736842105$$