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

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

Evaluer

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

Løsningsvejledning

Multiplicer 1 og 5 for at få 5.

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

Tilføj 5 og 3 for at få 8.

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

Subtraher \frac{8}{5} fra 2 for at få \frac{2}{5}.

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

Beregn \frac{2}{5} til potensen af 2, og få \frac{4}{25}.

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

Tilføj \frac{4}{25} og \frac{5}{8} for at få \frac{157}{200}.

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

Subtraher \frac{3}{4} fra \frac{157}{200} for at få \frac{7}{200}.

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

Multiplicer \frac{6}{5} og \frac{1}{3} for at få \frac{2}{5}.

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

Beregn \frac{2}{5} til potensen af 4, og få \frac{16}{625}.

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

Multiplicer 7 og 2 for at få 14.

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

Tilføj 14 og 1 for at få 15.

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

Beregn \frac{15}{2} til potensen af 3, og få \frac{3375}{8}.

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

Multiplicer \frac{16}{625} og \frac{3375}{8} for at få \frac{54}{5}.

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

Subtraher \frac{54}{5} fra \frac{7}{200} for at få -\frac{2153}{200}.

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

Subtraher \frac{6}{5} fra 5 for at få \frac{19}{5}.

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

Divider -\frac{2153}{200} med \frac{19}{5} ved at multiplicere -\frac{2153}{200} med den reciprokke værdi af \frac{19}{5}.

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

Multiplicer -\frac{2153}{200} og \frac{5}{19} for at få -\frac{2153}{760}.

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

Faktoriser

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