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

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

I-evaluate

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

Mga Hakbang ng Solution

I-multiply ang 1 at 5 para makuha ang 5.

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

Idagdag ang 5 at 3 para makuha ang 8.

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

I-subtract ang \frac{8}{5} mula sa 2 para makuha ang \frac{2}{5}.

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

Kalkulahin ang \frac{2}{5} sa power ng 2 at kunin ang \frac{4}{25}.

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

Idagdag ang \frac{4}{25} at \frac{5}{8} para makuha ang \frac{157}{200}.

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

I-subtract ang \frac{3}{4} mula sa \frac{157}{200} para makuha ang \frac{7}{200}.

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

I-multiply ang \frac{6}{5} at \frac{1}{3} para makuha ang \frac{2}{5}.

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

Kalkulahin ang \frac{2}{5} sa power ng 4 at kunin ang \frac{16}{625}.

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

I-multiply ang 7 at 2 para makuha ang 14.

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

Idagdag ang 14 at 1 para makuha ang 15.

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

Kalkulahin ang \frac{15}{2} sa power ng 3 at kunin ang \frac{3375}{8}.

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

I-multiply ang \frac{16}{625} at \frac{3375}{8} para makuha ang \frac{54}{5}.

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

I-subtract ang \frac{54}{5} mula sa \frac{7}{200} para makuha ang -\frac{2153}{200}.

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

I-subtract ang \frac{6}{5} mula sa 5 para makuha ang \frac{19}{5}.

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

I-divide ang -\frac{2153}{200} gamit ang \frac{19}{5} sa pamamagitan ng pagmu-multiply sa -\frac{2153}{200} gamit ang reciprocal ng \frac{19}{5}.

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

I-multiply ang -\frac{2153}{200} at \frac{5}{19} para makuha ang -\frac{2153}{760}.

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

I-factor

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