Ratkaise [(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

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

Laske

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

Ratkaisun vaiheet

Jos haluat kertoa samankantaiset potenssit, lisää niiden eksponentit yhteen. Lisää 3 ja 4 yhteen saadaksesi 7.

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

Laske \frac{2}{3} potenssiin 2, jolloin ratkaisuksi tulee \frac{4}{9}.

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

Laske -\frac{2}{3} potenssiin 7, jolloin ratkaisuksi tulee -\frac{128}{2187}.

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

Kerro \frac{4}{9} ja -\frac{128}{2187}, niin saadaan -\frac{512}{19683}.

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

Laske -\frac{512}{19683} potenssiin 2, jolloin ratkaisuksi tulee \frac{262144}{387420489}.

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

Laske -\frac{2}{3} potenssiin 5, jolloin ratkaisuksi tulee -\frac{32}{243}.

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

Luvun -\frac{32}{243} vastaluku on \frac{32}{243}.

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

Laske \frac{32}{243} potenssiin 3, jolloin ratkaisuksi tulee \frac{32768}{14348907}.

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

Jaa \frac{262144}{387420489} luvulla \frac{32768}{14348907} kertomalla \frac{262144}{387420489} luvun \frac{32768}{14348907} käänteisluvulla.

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

Kerro \frac{262144}{387420489} ja \frac{14348907}{32768}, niin saadaan \frac{8}{27}.

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

Laske -\frac{2}{3} potenssiin 3, jolloin ratkaisuksi tulee -\frac{8}{27}.

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

Vähennä \frac{8}{27} luvusta \frac{8}{27} saadaksesi tuloksen 0.

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

Laske \frac{2}{7} potenssiin 4, jolloin ratkaisuksi tulee \frac{16}{2401}.

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

Laske -\frac{7}{4} potenssiin 4, jolloin ratkaisuksi tulee \frac{2401}{256}.

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

Kerro \frac{16}{2401} ja \frac{2401}{256}, niin saadaan \frac{1}{16}.

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

Vähennä \frac{1}{16} luvusta 0 saadaksesi tuloksen -\frac{1}{16}.

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

Jaa tekijöihin

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