Atrisiniet [(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

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

Izrēķināt

$$-\frac{1}{16}=-0,0625$$

Atrisinājuma darbības

Lai reizinātu vienas bāzes pakāpes, saskaitiet kāpinātājus. Saskaitiet 3 un 4, lai iegūtu 7.

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

Aprēķiniet \frac{2}{3} pakāpē 2 un iegūstiet \frac{4}{9}.

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

Aprēķiniet -\frac{2}{3} pakāpē 7 un iegūstiet -\frac{128}{2187}.

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

Reiziniet \frac{4}{9} un -\frac{128}{2187}, lai iegūtu -\frac{512}{19683}.

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

Aprēķiniet -\frac{512}{19683} pakāpē 2 un iegūstiet \frac{262144}{387420489}.

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

Aprēķiniet -\frac{2}{3} pakāpē 5 un iegūstiet -\frac{32}{243}.

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

Skaitļa -\frac{32}{243} pretstats ir \frac{32}{243}.

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

Aprēķiniet \frac{32}{243} pakāpē 3 un iegūstiet \frac{32768}{14348907}.

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

Daliet \frac{262144}{387420489} ar \frac{32768}{14348907}, reizinot \frac{262144}{387420489} ar apgriezto daļskaitli \frac{32768}{14348907} .

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

Reiziniet \frac{262144}{387420489} un \frac{14348907}{32768}, lai iegūtu \frac{8}{27}.

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

Aprēķiniet -\frac{2}{3} pakāpē 3 un iegūstiet -\frac{8}{27}.

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

Atņemiet \frac{8}{27} no \frac{8}{27}, lai iegūtu 0.

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

Aprēķiniet \frac{2}{7} pakāpē 4 un iegūstiet \frac{16}{2401}.

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

Aprēķiniet -\frac{7}{4} pakāpē 4 un iegūstiet \frac{2401}{256}.

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

Reiziniet \frac{16}{2401} un \frac{2401}{256}, lai iegūtu \frac{1}{16}.

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

Atņemiet \frac{1}{16} no 0, lai iegūtu -\frac{1}{16}.

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

Sadalīt reizinātājos

$$-\frac{1}{16} = -0,0625$$