Rešite {[(-3/5)^{6}*(25/9)^2]^4:(9/5)^6*27^2}:(-3/25)

$$\{ [ ( - \frac { 3 } { 5 } ) ^ { 6 } \cdot ( \frac { 25 } { 9 } ) ^ { 2 } ] ^ { 4 } : ( \frac { 9 } { 5 } ) ^ { 6 } \cdot 27 ^ { 2 } \} : ( - \frac { 3 } { 25 } )$$

Ovrednoti

$$-3$$

Koraki rešitve

Izračunajte potenco -\frac{3}{5} števila 6, da dobite \frac{729}{15625}.

$$\frac{\frac{\left(\frac{729}{15625}\times \left(\frac{25}{9}\right)^{2}\right)^{4}}{\left(\frac{9}{5}\right)^{6}}\times 27^{2}}{-\frac{3}{25}}$$

Izračunajte potenco \frac{25}{9} števila 2, da dobite \frac{625}{81}.

$$\frac{\frac{\left(\frac{729}{15625}\times \frac{625}{81}\right)^{4}}{\left(\frac{9}{5}\right)^{6}}\times 27^{2}}{-\frac{3}{25}}$$

Pomnožite \frac{729}{15625} in \frac{625}{81}, da dobite \frac{9}{25}.

$$\frac{\frac{\left(\frac{9}{25}\right)^{4}}{\left(\frac{9}{5}\right)^{6}}\times 27^{2}}{-\frac{3}{25}}$$

Izračunajte potenco \frac{9}{25} števila 4, da dobite \frac{6561}{390625}.

$$\frac{\frac{\frac{6561}{390625}}{\left(\frac{9}{5}\right)^{6}}\times 27^{2}}{-\frac{3}{25}}$$

Izračunajte potenco \frac{9}{5} števila 6, da dobite \frac{531441}{15625}.

$$\frac{\frac{\frac{6561}{390625}}{\frac{531441}{15625}}\times 27^{2}}{-\frac{3}{25}}$$

Delite \frac{6561}{390625} s/z \frac{531441}{15625} tako, da pomnožite \frac{6561}{390625} z obratno vrednostjo \frac{531441}{15625}.

$$\frac{\frac{6561}{390625}\times \frac{15625}{531441}\times 27^{2}}{-\frac{3}{25}}$$

Pomnožite \frac{6561}{390625} in \frac{15625}{531441}, da dobite \frac{1}{2025}.

$$\frac{\frac{1}{2025}\times 27^{2}}{-\frac{3}{25}}$$

Izračunajte potenco 27 števila 2, da dobite 729.

$$\frac{\frac{1}{2025}\times 729}{-\frac{3}{25}}$$

Pomnožite \frac{1}{2025} in 729, da dobite \frac{9}{25}.

$$\frac{\frac{9}{25}}{-\frac{3}{25}}$$

Delite \frac{9}{25} s/z -\frac{3}{25} tako, da pomnožite \frac{9}{25} z obratno vrednostjo -\frac{3}{25}.

$$\frac{9}{25}\left(-\frac{25}{3}\right)$$

Pomnožite \frac{9}{25} in -\frac{25}{3}, da dobite -3.

$$-3$$

Faktoriziraj

$$-3$$