Rešite (2/3)^{-4}*(2/3)^{-3}*(-3/2)^-5+8[(2-1/4)frac{1}{7}-frac{3}{4}]+[(-frac{3}{2})^2*(frac{1}{3})^2]^-1

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

Ovrednoti

$$-\frac{9}{4}=-2,25$$

Koraki rešitve

Če želite pomnožiti potence z isto osnovo, seštejte njihove eksponente. Seštejte -4 in -3, da dobite -7.

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

Izračunajte potenco \frac{2}{3} števila -7, da dobite \frac{2187}{128}.

$$\frac{2187}{128}\left(-\frac{3}{2}\right)^{-5}+8\left(\left(2-\frac{1}{4}\right)\times \frac{1}{7}-\frac{3}{4}\right)+\left(\left(-\frac{3}{2}\right)^{2}\times \left(\frac{1}{3}\right)^{2}\right)^{-1}$$

Izračunajte potenco -\frac{3}{2} števila -5, da dobite -\frac{32}{243}.

$$\frac{2187}{128}\left(-\frac{32}{243}\right)+8\left(\left(2-\frac{1}{4}\right)\times \frac{1}{7}-\frac{3}{4}\right)+\left(\left(-\frac{3}{2}\right)^{2}\times \left(\frac{1}{3}\right)^{2}\right)^{-1}$$

Pomnožite \frac{2187}{128} in -\frac{32}{243}, da dobite -\frac{9}{4}.

$$-\frac{9}{4}+8\left(\left(2-\frac{1}{4}\right)\times \frac{1}{7}-\frac{3}{4}\right)+\left(\left(-\frac{3}{2}\right)^{2}\times \left(\frac{1}{3}\right)^{2}\right)^{-1}$$

Odštejte \frac{1}{4} od 2, da dobite \frac{7}{4}.

$$-\frac{9}{4}+8\left(\frac{7}{4}\times \frac{1}{7}-\frac{3}{4}\right)+\left(\left(-\frac{3}{2}\right)^{2}\times \left(\frac{1}{3}\right)^{2}\right)^{-1}$$

Pomnožite \frac{7}{4} in \frac{1}{7}, da dobite \frac{1}{4}.

$$-\frac{9}{4}+8\left(\frac{1}{4}-\frac{3}{4}\right)+\left(\left(-\frac{3}{2}\right)^{2}\times \left(\frac{1}{3}\right)^{2}\right)^{-1}$$

Odštejte \frac{3}{4} od \frac{1}{4}, da dobite -\frac{1}{2}.

$$-\frac{9}{4}+8\left(-\frac{1}{2}\right)+\left(\left(-\frac{3}{2}\right)^{2}\times \left(\frac{1}{3}\right)^{2}\right)^{-1}$$

Pomnožite 8 in -\frac{1}{2}, da dobite -4.

$$-\frac{9}{4}-4+\left(\left(-\frac{3}{2}\right)^{2}\times \left(\frac{1}{3}\right)^{2}\right)^{-1}$$

Odštejte 4 od -\frac{9}{4}, da dobite -\frac{25}{4}.

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

Izračunajte potenco -\frac{3}{2} števila 2, da dobite \frac{9}{4}.

$$-\frac{25}{4}+\left(\frac{9}{4}\times \left(\frac{1}{3}\right)^{2}\right)^{-1}$$

Izračunajte potenco \frac{1}{3} števila 2, da dobite \frac{1}{9}.

$$-\frac{25}{4}+\left(\frac{9}{4}\times \frac{1}{9}\right)^{-1}$$

Pomnožite \frac{9}{4} in \frac{1}{9}, da dobite \frac{1}{4}.

$$-\frac{25}{4}+\left(\frac{1}{4}\right)^{-1}$$

Izračunajte potenco \frac{1}{4} števila -1, da dobite 4.

$$-\frac{25}{4}+4$$

Seštejte -\frac{25}{4} in 4, da dobite -\frac{9}{4}.

$$-\frac{9}{4}$$

Faktoriziraj

$$-\frac{9}{4} = -2\frac{1}{4} = -2,25$$