Rešite [4/5a^{3}b^{4}c:(-2/5ab^{2})]^{2}+(-2a^{2}bc)^{2}*(-7b^2)+23a^4b^4c^2

$$[ \frac { 4 } { 5 } a ^ { 3 } b ^ { 4 } c : ( - \frac { 2 } { 5 } a b ^ { 2 } ) ] ^ { 2 } + ( - 2 a ^ { 2 } b c ) ^ { 2 } \cdot ( - 7 b ^ { 2 } ) + 23 a ^ { 4 } b ^ { 4 } c ^ { 2 }$$

Ovrednoti

$$-c^{2}\left(ab\right)^{4}$$

Koraki rešitve

Okrajšaj ab^{2} v števcu in imenovalcu.

$$\left(\frac{\frac{4}{5}ca^{2}b^{2}}{-\frac{2}{5}}\right)^{2}+\left(-2a^{2}bc\right)^{2}\left(-7\right)b^{2}+23a^{4}b^{4}c^{2}$$

Delite \frac{4}{5}ca^{2}b^{2} s/z -\frac{2}{5} tako, da pomnožite \frac{4}{5}ca^{2}b^{2} z obratno vrednostjo -\frac{2}{5}.

$$\left(\frac{\frac{4}{5}ca^{2}b^{2}\times 5}{-2}\right)^{2}+\left(-2a^{2}bc\right)^{2}\left(-7\right)b^{2}+23a^{4}b^{4}c^{2}$$

Pomnožite \frac{4}{5} in 5, da dobite 4.

$$\left(\frac{4ca^{2}b^{2}}{-2}\right)^{2}+\left(-2a^{2}bc\right)^{2}\left(-7\right)b^{2}+23a^{4}b^{4}c^{2}$$

Delite 4ca^{2}b^{2} s/z -2, da dobite -2ca^{2}b^{2}.

$$\left(-2ca^{2}b^{2}\right)^{2}+\left(-2a^{2}bc\right)^{2}\left(-7\right)b^{2}+23a^{4}b^{4}c^{2}$$

Razčlenite \left(-2ca^{2}b^{2}\right)^{2}.

$$\left(-2\right)^{2}c^{2}\left(a^{2}\right)^{2}\left(b^{2}\right)^{2}+\left(-2a^{2}bc\right)^{2}\left(-7\right)b^{2}+23a^{4}b^{4}c^{2}$$

Če želite potenco potencirati z drugo potenco, pomnožite eksponente. Pomnožite 2 in 2, da dobite 4.

$$\left(-2\right)^{2}c^{2}a^{4}\left(b^{2}\right)^{2}+\left(-2a^{2}bc\right)^{2}\left(-7\right)b^{2}+23a^{4}b^{4}c^{2}$$

Če želite potenco potencirati z drugo potenco, pomnožite eksponente. Pomnožite 2 in 2, da dobite 4.

$$\left(-2\right)^{2}c^{2}a^{4}b^{4}+\left(-2a^{2}bc\right)^{2}\left(-7\right)b^{2}+23a^{4}b^{4}c^{2}$$

Izračunajte potenco -2 števila 2, da dobite 4.

$$4c^{2}a^{4}b^{4}+\left(-2a^{2}bc\right)^{2}\left(-7\right)b^{2}+23a^{4}b^{4}c^{2}$$

Razčlenite \left(-2a^{2}bc\right)^{2}.

$$4c^{2}a^{4}b^{4}+\left(-2\right)^{2}\left(a^{2}\right)^{2}b^{2}c^{2}\left(-7\right)b^{2}+23a^{4}b^{4}c^{2}$$

Če želite potenco potencirati z drugo potenco, pomnožite eksponente. Pomnožite 2 in 2, da dobite 4.

$$4c^{2}a^{4}b^{4}+\left(-2\right)^{2}a^{4}b^{2}c^{2}\left(-7\right)b^{2}+23a^{4}b^{4}c^{2}$$

Izračunajte potenco -2 števila 2, da dobite 4.

$$4c^{2}a^{4}b^{4}+4a^{4}b^{2}c^{2}\left(-7\right)b^{2}+23a^{4}b^{4}c^{2}$$

Pomnožite 4 in -7, da dobite -28.

$$4c^{2}a^{4}b^{4}-28a^{4}b^{2}c^{2}b^{2}+23a^{4}b^{4}c^{2}$$

Če želite pomnožiti potence z isto osnovo, seštejte njihove eksponente. Seštejte 2 in 2, da dobite 4.

$$4c^{2}a^{4}b^{4}-28a^{4}b^{4}c^{2}+23a^{4}b^{4}c^{2}$$

Združite 4c^{2}a^{4}b^{4} in -28a^{4}b^{4}c^{2}, da dobite -24c^{2}a^{4}b^{4}.

$$-24c^{2}a^{4}b^{4}+23a^{4}b^{4}c^{2}$$

Združite -24c^{2}a^{4}b^{4} in 23a^{4}b^{4}c^{2}, da dobite -c^{2}a^{4}b^{4}.

$$-c^{2}a^{4}b^{4}$$

Razširi

$$-c^{2}\left(ab\right)^{4}$$

Koraki rešitve

Okrajšaj ab^{2} v števcu in imenovalcu.

$$\left(\frac{\frac{4}{5}ca^{2}b^{2}}{-\frac{2}{5}}\right)^{2}+\left(-2a^{2}bc\right)^{2}\left(-7\right)b^{2}+23a^{4}b^{4}c^{2}$$

Delite \frac{4}{5}ca^{2}b^{2} s/z -\frac{2}{5} tako, da pomnožite \frac{4}{5}ca^{2}b^{2} z obratno vrednostjo -\frac{2}{5}.

$$\left(\frac{\frac{4}{5}ca^{2}b^{2}\times 5}{-2}\right)^{2}+\left(-2a^{2}bc\right)^{2}\left(-7\right)b^{2}+23a^{4}b^{4}c^{2}$$

Pomnožite \frac{4}{5} in 5, da dobite 4.

$$\left(\frac{4ca^{2}b^{2}}{-2}\right)^{2}+\left(-2a^{2}bc\right)^{2}\left(-7\right)b^{2}+23a^{4}b^{4}c^{2}$$

Delite 4ca^{2}b^{2} s/z -2, da dobite -2ca^{2}b^{2}.

$$\left(-2ca^{2}b^{2}\right)^{2}+\left(-2a^{2}bc\right)^{2}\left(-7\right)b^{2}+23a^{4}b^{4}c^{2}$$

Razčlenite \left(-2ca^{2}b^{2}\right)^{2}.

$$\left(-2\right)^{2}c^{2}\left(a^{2}\right)^{2}\left(b^{2}\right)^{2}+\left(-2a^{2}bc\right)^{2}\left(-7\right)b^{2}+23a^{4}b^{4}c^{2}$$

Če želite potenco potencirati z drugo potenco, pomnožite eksponente. Pomnožite 2 in 2, da dobite 4.

$$\left(-2\right)^{2}c^{2}a^{4}\left(b^{2}\right)^{2}+\left(-2a^{2}bc\right)^{2}\left(-7\right)b^{2}+23a^{4}b^{4}c^{2}$$

Če želite potenco potencirati z drugo potenco, pomnožite eksponente. Pomnožite 2 in 2, da dobite 4.

$$\left(-2\right)^{2}c^{2}a^{4}b^{4}+\left(-2a^{2}bc\right)^{2}\left(-7\right)b^{2}+23a^{4}b^{4}c^{2}$$

Izračunajte potenco -2 števila 2, da dobite 4.

$$4c^{2}a^{4}b^{4}+\left(-2a^{2}bc\right)^{2}\left(-7\right)b^{2}+23a^{4}b^{4}c^{2}$$

Razčlenite \left(-2a^{2}bc\right)^{2}.

$$4c^{2}a^{4}b^{4}+\left(-2\right)^{2}\left(a^{2}\right)^{2}b^{2}c^{2}\left(-7\right)b^{2}+23a^{4}b^{4}c^{2}$$

Če želite potenco potencirati z drugo potenco, pomnožite eksponente. Pomnožite 2 in 2, da dobite 4.

$$4c^{2}a^{4}b^{4}+\left(-2\right)^{2}a^{4}b^{2}c^{2}\left(-7\right)b^{2}+23a^{4}b^{4}c^{2}$$

Izračunajte potenco -2 števila 2, da dobite 4.

$$4c^{2}a^{4}b^{4}+4a^{4}b^{2}c^{2}\left(-7\right)b^{2}+23a^{4}b^{4}c^{2}$$

Pomnožite 4 in -7, da dobite -28.

$$4c^{2}a^{4}b^{4}-28a^{4}b^{2}c^{2}b^{2}+23a^{4}b^{4}c^{2}$$

Če želite pomnožiti potence z isto osnovo, seštejte njihove eksponente. Seštejte 2 in 2, da dobite 4.

$$4c^{2}a^{4}b^{4}-28a^{4}b^{4}c^{2}+23a^{4}b^{4}c^{2}$$

Združite 4c^{2}a^{4}b^{4} in -28a^{4}b^{4}c^{2}, da dobite -24c^{2}a^{4}b^{4}.

$$-24c^{2}a^{4}b^{4}+23a^{4}b^{4}c^{2}$$

Združite -24c^{2}a^{4}b^{4} in 23a^{4}b^{4}c^{2}, da dobite -c^{2}a^{4}b^{4}.

$$-c^{2}a^{4}b^{4}$$