Lahenda frac{[(125)^{-2}*8^{-3}]^{-1}}{[25^{3}*16]^{-2}}div[5^-3*3^2-1]^-1/[64*25]^2

$$\frac { [ ( 125 ) ^ { - 2 } \cdot 8 ^ { - 3 } ] ^ { - 1 } } { [ 25 ^ { 3 } \cdot 16 ] ^ { - 2 } } \div \frac { [ 5 ^ { - 3 } \cdot 3 ^ { 2 } - 1 ] ^ { - 1 } } { [ 64 \cdot 25 ] ^ { 2 } }$$

Arvuta

$$-1187840000000000000000000$$

Lahenduse etapid

Jagage \frac{\left(125^{-2}\times 8^{-3}\right)^{-1}}{\left(25^{3}\times 16\right)^{-2}} väärtusega \frac{\left(5^{-3}\times 3^{2}-1\right)^{-1}}{\left(64\times 25\right)^{2}}, korrutades \frac{\left(125^{-2}\times 8^{-3}\right)^{-1}}{\left(25^{3}\times 16\right)^{-2}} väärtuse \frac{\left(5^{-3}\times 3^{2}-1\right)^{-1}}{\left(64\times 25\right)^{2}} pöördväärtusega.

$$\frac{\left(125^{-2}\times 8^{-3}\right)^{-1}\times \left(64\times 25\right)^{2}}{\left(25^{3}\times 16\right)^{-2}\left(5^{-3}\times 3^{2}-1\right)^{-1}}$$

Arvutage -2 aste 125 ja leidke \frac{1}{15625}.

$$\frac{\left(\frac{1}{15625}\times 8^{-3}\right)^{-1}\times \left(64\times 25\right)^{2}}{\left(25^{3}\times 16\right)^{-2}\left(5^{-3}\times 3^{2}-1\right)^{-1}}$$

Arvutage -3 aste 8 ja leidke \frac{1}{512}.

$$\frac{\left(\frac{1}{15625}\times \frac{1}{512}\right)^{-1}\times \left(64\times 25\right)^{2}}{\left(25^{3}\times 16\right)^{-2}\left(5^{-3}\times 3^{2}-1\right)^{-1}}$$

Korrutage \frac{1}{15625} ja \frac{1}{512}, et leida \frac{1}{8000000}.

$$\frac{\left(\frac{1}{8000000}\right)^{-1}\times \left(64\times 25\right)^{2}}{\left(25^{3}\times 16\right)^{-2}\left(5^{-3}\times 3^{2}-1\right)^{-1}}$$

Arvutage -1 aste \frac{1}{8000000} ja leidke 8000000.

$$\frac{8000000\times \left(64\times 25\right)^{2}}{\left(25^{3}\times 16\right)^{-2}\left(5^{-3}\times 3^{2}-1\right)^{-1}}$$

Korrutage 64 ja 25, et leida 1600.

$$\frac{8000000\times 1600^{2}}{\left(25^{3}\times 16\right)^{-2}\left(5^{-3}\times 3^{2}-1\right)^{-1}}$$

Arvutage 2 aste 1600 ja leidke 2560000.

$$\frac{8000000\times 2560000}{\left(25^{3}\times 16\right)^{-2}\left(5^{-3}\times 3^{2}-1\right)^{-1}}$$

Korrutage 8000000 ja 2560000, et leida 20480000000000.

$$\frac{20480000000000}{\left(25^{3}\times 16\right)^{-2}\left(5^{-3}\times 3^{2}-1\right)^{-1}}$$

Arvutage 3 aste 25 ja leidke 15625.

$$\frac{20480000000000}{\left(15625\times 16\right)^{-2}\left(5^{-3}\times 3^{2}-1\right)^{-1}}$$

Korrutage 15625 ja 16, et leida 250000.

$$\frac{20480000000000}{250000^{-2}\left(5^{-3}\times 3^{2}-1\right)^{-1}}$$

Arvutage -2 aste 250000 ja leidke \frac{1}{62500000000}.

$$\frac{20480000000000}{\frac{1}{62500000000}\left(5^{-3}\times 3^{2}-1\right)^{-1}}$$

Arvutage -3 aste 5 ja leidke \frac{1}{125}.

$$\frac{20480000000000}{\frac{1}{62500000000}\left(\frac{1}{125}\times 3^{2}-1\right)^{-1}}$$

Arvutage 2 aste 3 ja leidke 9.

$$\frac{20480000000000}{\frac{1}{62500000000}\left(\frac{1}{125}\times 9-1\right)^{-1}}$$

Korrutage \frac{1}{125} ja 9, et leida \frac{9}{125}.

$$\frac{20480000000000}{\frac{1}{62500000000}\left(\frac{9}{125}-1\right)^{-1}}$$

Lahutage 1 väärtusest \frac{9}{125}, et leida -\frac{116}{125}.

$$\frac{20480000000000}{\frac{1}{62500000000}\left(-\frac{116}{125}\right)^{-1}}$$

Arvutage -1 aste -\frac{116}{125} ja leidke -\frac{125}{116}.

$$\frac{20480000000000}{\frac{1}{62500000000}\left(-\frac{125}{116}\right)}$$

Korrutage \frac{1}{62500000000} ja -\frac{125}{116}, et leida -\frac{1}{58000000000}.

$$\frac{20480000000000}{-\frac{1}{58000000000}}$$

Jagage 20480000000000 väärtusega -\frac{1}{58000000000}, korrutades 20480000000000 väärtuse -\frac{1}{58000000000} pöördväärtusega.

$$20480000000000\left(-58000000000\right)$$

Korrutage 20480000000000 ja -58000000000, et leida -1187840000000000000000000.

$$-1187840000000000000000000$$

Lahuta teguriteks

$$-1187840000000000000000000$$