Lahenda frac{(-27)^{3}(32)^{-2}(-8)^{4}(25^2)}{(-72)^4(-50^3)^4}

$$\frac { ( - 27 ) ^ { 3 } ( 32 ) ^ { - 2 } ( - 8 ) ^ { 4 } ( 25 ^ { 2 } ) } { ( - 72 ) ^ { 4 } ( - 50 ^ { 3 } ) ^ { 4 } }$$

Arvuta

$$-\frac{3}{400000000000000000000}=-7,5 \cdot 10^{-21}$$

Lahenduse etapid

Arvutage 3 aste -27 ja leidke -19683.

$$\frac{-19683\times 32^{-2}\left(-8\right)^{4}\times 25^{2}}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

Arvutage -2 aste 32 ja leidke \frac{1}{1024}.

$$\frac{-19683\times \frac{1}{1024}\left(-8\right)^{4}\times 25^{2}}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

Korrutage -19683 ja \frac{1}{1024}, et leida -\frac{19683}{1024}.

$$\frac{-\frac{19683}{1024}\left(-8\right)^{4}\times 25^{2}}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

Arvutage 4 aste -8 ja leidke 4096.

$$\frac{-\frac{19683}{1024}\times 4096\times 25^{2}}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

Korrutage -\frac{19683}{1024} ja 4096, et leida -78732.

$$\frac{-78732\times 25^{2}}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

Arvutage 2 aste 25 ja leidke 625.

$$\frac{-78732\times 625}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

Korrutage -78732 ja 625, et leida -49207500.

$$\frac{-49207500}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

Arvutage 4 aste -72 ja leidke 26873856.

$$\frac{-49207500}{26873856\left(-50^{3}\right)^{4}}$$

Arvutage 3 aste 50 ja leidke 125000.

$$\frac{-49207500}{26873856\left(-125000\right)^{4}}$$

Arvutage 4 aste -125000 ja leidke 244140625000000000000.

$$\frac{-49207500}{26873856\times 244140625000000000000}$$

Korrutage 26873856 ja 244140625000000000000, et leida 6561000000000000000000000000.

$$\frac{-49207500}{6561000000000000000000000000}$$

Taandage murd \frac{-49207500}{6561000000000000000000000000} vähimale ühiskordsele, eraldades ja taandades arvu 16402500.

$$-\frac{3}{400000000000000000000}$$

Lahuta teguriteks

$$-\frac{3}{400000000000000000000} = -7,500000000000002 \times 10^{-21}$$