Réitigh [(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

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

Luacháil

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

Céimeanna Réitigh

Chun cumhachtaí den bhonn céanna a iolrú, suimigh a n-easpónaint. Suimigh 3 agus 4 chun 7 a bhaint amach.

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

Ríomh cumhacht \frac{2}{3} de 2 agus faigh \frac{4}{9}.

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

Ríomh cumhacht -\frac{2}{3} de 7 agus faigh -\frac{128}{2187}.

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

Méadaigh \frac{4}{9} agus -\frac{128}{2187} chun -\frac{512}{19683} a fháil.

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

Ríomh cumhacht -\frac{512}{19683} de 2 agus faigh \frac{262144}{387420489}.

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

Ríomh cumhacht -\frac{2}{3} de 5 agus faigh -\frac{32}{243}.

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

Tá \frac{32}{243} urchomhairleach le -\frac{32}{243}.

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

Ríomh cumhacht \frac{32}{243} de 3 agus faigh \frac{32768}{14348907}.

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

Roinn \frac{262144}{387420489} faoi \frac{32768}{14348907} trí \frac{262144}{387420489} a mhéadú faoi dheilín \frac{32768}{14348907}.

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

Méadaigh \frac{262144}{387420489} agus \frac{14348907}{32768} chun \frac{8}{27} a fháil.

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

Ríomh cumhacht -\frac{2}{3} de 3 agus faigh -\frac{8}{27}.

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

Dealaigh \frac{8}{27} ó \frac{8}{27} chun 0 a fháil.

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

Ríomh cumhacht \frac{2}{7} de 4 agus faigh \frac{16}{2401}.

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

Ríomh cumhacht -\frac{7}{4} de 4 agus faigh \frac{2401}{256}.

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

Méadaigh \frac{16}{2401} agus \frac{2401}{256} chun \frac{1}{16} a fháil.

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

Dealaigh \frac{1}{16} ó 0 chun -\frac{1}{16} a fháil.

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

Fachtóirigh

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