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

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

I-evaluate

$$-\frac{1}{16}=-0.0625$$

Mga Hakbang ng Solution

Para mag-multiply ng mga power na may parehong base, i-add ang mga exponent ng mga ito. I-add ang 3 at 4 para makuha ang 7.

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

Kalkulahin ang \frac{2}{3} sa power ng 2 at kunin ang \frac{4}{9}.

$$\frac{\left(\frac{4}{9}\left(-\frac{2}{3}\right)^{7}\right)^{2}}{\left(-\left(-\frac{2}{3}\right)^{5}\right)^{3}}+\left(-\frac{2}{3}\right)^{3}-\left(\frac{2}{7}\right)^{4}\left(-\frac{7}{4}\right)^{4}$$

Kalkulahin ang -\frac{2}{3} sa power ng 7 at kunin ang -\frac{128}{2187}.

$$\frac{\left(\frac{4}{9}\left(-\frac{128}{2187}\right)\right)^{2}}{\left(-\left(-\frac{2}{3}\right)^{5}\right)^{3}}+\left(-\frac{2}{3}\right)^{3}-\left(\frac{2}{7}\right)^{4}\left(-\frac{7}{4}\right)^{4}$$

I-multiply ang \frac{4}{9} at -\frac{128}{2187} para makuha ang -\frac{512}{19683}.

$$\frac{\left(-\frac{512}{19683}\right)^{2}}{\left(-\left(-\frac{2}{3}\right)^{5}\right)^{3}}+\left(-\frac{2}{3}\right)^{3}-\left(\frac{2}{7}\right)^{4}\left(-\frac{7}{4}\right)^{4}$$

Kalkulahin ang -\frac{512}{19683} sa power ng 2 at kunin ang \frac{262144}{387420489}.

$$\frac{\frac{262144}{387420489}}{\left(-\left(-\frac{2}{3}\right)^{5}\right)^{3}}+\left(-\frac{2}{3}\right)^{3}-\left(\frac{2}{7}\right)^{4}\left(-\frac{7}{4}\right)^{4}$$

Kalkulahin ang -\frac{2}{3} sa power ng 5 at kunin ang -\frac{32}{243}.

$$\frac{\frac{262144}{387420489}}{\left(-\left(-\frac{32}{243}\right)\right)^{3}}+\left(-\frac{2}{3}\right)^{3}-\left(\frac{2}{7}\right)^{4}\left(-\frac{7}{4}\right)^{4}$$

Ang kabaliktaran ng -\frac{32}{243} ay \frac{32}{243}.

$$\frac{\frac{262144}{387420489}}{\left(\frac{32}{243}\right)^{3}}+\left(-\frac{2}{3}\right)^{3}-\left(\frac{2}{7}\right)^{4}\left(-\frac{7}{4}\right)^{4}$$

Kalkulahin ang \frac{32}{243} sa power ng 3 at kunin ang \frac{32768}{14348907}.

$$\frac{\frac{262144}{387420489}}{\frac{32768}{14348907}}+\left(-\frac{2}{3}\right)^{3}-\left(\frac{2}{7}\right)^{4}\left(-\frac{7}{4}\right)^{4}$$

I-divide ang \frac{262144}{387420489} gamit ang \frac{32768}{14348907} sa pamamagitan ng pagmu-multiply sa \frac{262144}{387420489} gamit ang reciprocal ng \frac{32768}{14348907}.

$$\frac{262144}{387420489}\times \frac{14348907}{32768}+\left(-\frac{2}{3}\right)^{3}-\left(\frac{2}{7}\right)^{4}\left(-\frac{7}{4}\right)^{4}$$

I-multiply ang \frac{262144}{387420489} at \frac{14348907}{32768} para makuha ang \frac{8}{27}.

$$\frac{8}{27}+\left(-\frac{2}{3}\right)^{3}-\left(\frac{2}{7}\right)^{4}\left(-\frac{7}{4}\right)^{4}$$

Kalkulahin ang -\frac{2}{3} sa power ng 3 at kunin ang -\frac{8}{27}.

$$\frac{8}{27}-\frac{8}{27}-\left(\frac{2}{7}\right)^{4}\left(-\frac{7}{4}\right)^{4}$$

I-subtract ang \frac{8}{27} mula sa \frac{8}{27} para makuha ang 0.

$$0-\left(\frac{2}{7}\right)^{4}\left(-\frac{7}{4}\right)^{4}$$

Kalkulahin ang \frac{2}{7} sa power ng 4 at kunin ang \frac{16}{2401}.

$$0-\frac{16}{2401}\left(-\frac{7}{4}\right)^{4}$$

Kalkulahin ang -\frac{7}{4} sa power ng 4 at kunin ang \frac{2401}{256}.

$$0-\frac{16}{2401}\times \frac{2401}{256}$$

I-multiply ang \frac{16}{2401} at \frac{2401}{256} para makuha ang \frac{1}{16}.

$$0-\frac{1}{16}$$

I-subtract ang \frac{1}{16} mula sa 0 para makuha ang -\frac{1}{16}.

$$-\frac{1}{16}$$

I-factor

$$-\frac{1}{16} = -0.0625$$