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

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

Arvuta

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

Lahenduse etapid

Korrutage 1 ja 5, et leida 5.

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

Liitke 5 ja 3, et leida 8.

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

Lahutage \frac{8}{5} väärtusest 2, et leida \frac{2}{5}.

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

Arvutage 2 aste \frac{2}{5} ja leidke \frac{4}{25}.

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

Liitke \frac{4}{25} ja \frac{5}{8}, et leida \frac{157}{200}.

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

Lahutage \frac{3}{4} väärtusest \frac{157}{200}, et leida \frac{7}{200}.

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

Korrutage \frac{6}{5} ja \frac{1}{3}, et leida \frac{2}{5}.

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

Arvutage 4 aste \frac{2}{5} ja leidke \frac{16}{625}.

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

Korrutage 7 ja 2, et leida 14.

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

Liitke 14 ja 1, et leida 15.

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

Arvutage 3 aste \frac{15}{2} ja leidke \frac{3375}{8}.

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

Korrutage \frac{16}{625} ja \frac{3375}{8}, et leida \frac{54}{5}.

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

Lahutage \frac{54}{5} väärtusest \frac{7}{200}, et leida -\frac{2153}{200}.

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

Lahutage \frac{6}{5} väärtusest 5, et leida \frac{19}{5}.

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

Jagage -\frac{2153}{200} väärtusega \frac{19}{5}, korrutades -\frac{2153}{200} väärtuse \frac{19}{5} pöördväärtusega.

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

Korrutage -\frac{2153}{200} ja \frac{5}{19}, et leida -\frac{2153}{760}.

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

Lahuta teguriteks

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