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

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

Evalwa

$$-1187840000000000000000000$$

Passi tas-Soluzzjonijiet

Iddividi \frac{\left(125^{-2}\times 8^{-3}\right)^{-1}}{\left(25^{3}\times 16\right)^{-2}} b'\frac{\left(5^{-3}\times 3^{2}-1\right)^{-1}}{\left(64\times 25\right)^{2}} billi timmultiplika \frac{\left(125^{-2}\times 8^{-3}\right)^{-1}}{\left(25^{3}\times 16\right)^{-2}} bir-reċiproku ta' \frac{\left(5^{-3}\times 3^{2}-1\right)^{-1}}{\left(64\times 25\right)^{2}}.

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

Ikkalkula 125 bil-power ta' -2 u tikseb \frac{1}{15625}.

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

Ikkalkula 8 bil-power ta' -3 u tikseb \frac{1}{512}.

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

Immultiplika \frac{1}{15625} u \frac{1}{512} biex tikseb \frac{1}{8000000}.

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

Ikkalkula \frac{1}{8000000} bil-power ta' -1 u tikseb 8000000.

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

Immultiplika 64 u 25 biex tikseb 1600.

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

Ikkalkula 1600 bil-power ta' 2 u tikseb 2560000.

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

Immultiplika 8000000 u 2560000 biex tikseb 20480000000000.

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

Ikkalkula 25 bil-power ta' 3 u tikseb 15625.

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

Immultiplika 15625 u 16 biex tikseb 250000.

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

Ikkalkula 250000 bil-power ta' -2 u tikseb \frac{1}{62500000000}.

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

Ikkalkula 5 bil-power ta' -3 u tikseb \frac{1}{125}.

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

Ikkalkula 3 bil-power ta' 2 u tikseb 9.

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

Immultiplika \frac{1}{125} u 9 biex tikseb \frac{9}{125}.

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

Naqqas 1 minn \frac{9}{125} biex tikseb -\frac{116}{125}.

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

Ikkalkula -\frac{116}{125} bil-power ta' -1 u tikseb -\frac{125}{116}.

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

Immultiplika \frac{1}{62500000000} u -\frac{125}{116} biex tikseb -\frac{1}{58000000000}.

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

Iddividi 20480000000000 b'-\frac{1}{58000000000} billi timmultiplika 20480000000000 bir-reċiproku ta' -\frac{1}{58000000000}.

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

Immultiplika 20480000000000 u -58000000000 biex tikseb -1187840000000000000000000.

$$-1187840000000000000000000$$

Fattur

$$-1187840000000000000000000$$