Réitigh frac{frac{left(3^7.3right)^-42^2/3^4{2^{-2}-{4}^{2}}}{3/4{left(frac{2/3right)}^{2}2/6}{frac{{3}^{2}}{4}frac{{2}^{3}}{2}frac{{2}^{3}}{3}}}}{frac{frac{{3}^{4}-27-64}{{2}^{4}2{2}^{3}}}{frac{4*16*27{3}^{-2}}{{2}^6{3}^-2{3}^3{2}^6}}}

$$\frac{ \frac{ \frac{ { \left( { 3 }^{ 7 } .3 \right) }^{ -4 } { 2 }^{ 2 } }{ { 3 }^{ 4 } { 2 }^{ -2 } - { 4 }^{ 2 } } }{ \frac{ \frac{ 3 }{ 4 } { \left( \frac{ 2 }{ 3 } \right) }^{ 2 } \frac{ 2 }{ 6 } }{ \frac{ { 3 }^{ 2 } }{ 4 } \frac{ { 2 }^{ 3 } }{ 2 } \frac{ { 2 }^{ 3 } }{ 3 } } } }{ \frac{ \frac{ { 3 }^{ 4 } -27-64 }{ { 2 }^{ 4 } 2 { 2 }^{ 3 } } }{ \frac{ 4 \cdot 16 \cdot 27 { 3 }^{ -2 } }{ { 2 }^{ 6 } { 3 }^{ -2 } { 3 }^{ 3 } { 2 }^{ 6 } } } }$$

Luacháil

$$-\frac{512000}{1166716415203011}\approx -4.388384301 \cdot 10^{-10}$$

Céimeanna Réitigh

Chun cumhachtaí den bhonn céanna a roinnt, dealaigh easpónant an ainmneora ó easpónant an uimhreora. Dealaigh 1 ó 3 chun 2 a bhaint amach.

$$\frac{\frac{\frac{\left(3^{7}\times 0.3\right)^{-4}\times 2^{2}}{3^{4}\times 2^{-2}-4^{2}}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}}}{\frac{\frac{3^{4}-27-64}{2^{4}\times 2\times 2^{3}}}{\frac{4\times 16\times 27\times 3^{-2}}{2^{6}\times 3^{-2}\times 3^{3}\times 2^{6}}}}$$

Chun cumhachtaí den bhonn céanna a iolrú, suimigh a n-easpónaint. Suimigh 4 agus 1 chun 5 a bhaint amach.

$$\frac{\frac{\frac{\left(3^{7}\times 0.3\right)^{-4}\times 2^{2}}{3^{4}\times 2^{-2}-4^{2}}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}}}{\frac{\frac{3^{4}-27-64}{2^{5}\times 2^{3}}}{\frac{4\times 16\times 27\times 3^{-2}}{2^{6}\times 3^{-2}\times 3^{3}\times 2^{6}}}}$$

Chun cumhachtaí den bhonn céanna a iolrú, suimigh a n-easpónaint. Suimigh 5 agus 3 chun 8 a bhaint amach.

$$\frac{\frac{\frac{\left(3^{7}\times 0.3\right)^{-4}\times 2^{2}}{3^{4}\times 2^{-2}-4^{2}}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}}}{\frac{\frac{3^{4}-27-64}{2^{8}}}{\frac{4\times 16\times 27\times 3^{-2}}{2^{6}\times 3^{-2}\times 3^{3}\times 2^{6}}}}$$

Chun cumhachtaí den bhonn céanna a iolrú, suimigh a n-easpónaint. Suimigh 6 agus 6 chun 12 a bhaint amach.

$$\frac{\frac{\frac{\left(3^{7}\times 0.3\right)^{-4}\times 2^{2}}{3^{4}\times 2^{-2}-4^{2}}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}}}{\frac{\frac{3^{4}-27-64}{2^{8}}}{\frac{4\times 16\times 27\times 3^{-2}}{2^{12}\times 3^{-2}\times 3^{3}}}}$$

Chun cumhachtaí den bhonn céanna a iolrú, suimigh a n-easpónaint. Suimigh -2 agus 3 chun 1 a bhaint amach.

$$\frac{\frac{\frac{\left(3^{7}\times 0.3\right)^{-4}\times 2^{2}}{3^{4}\times 2^{-2}-4^{2}}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}}}{\frac{\frac{3^{4}-27-64}{2^{8}}}{\frac{4\times 16\times 27\times 3^{-2}}{2^{12}\times 3^{1}}}}$$

Roinn \frac{\frac{\left(3^{7}\times 0.3\right)^{-4}\times 2^{2}}{3^{4}\times 2^{-2}-4^{2}}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}} faoi \frac{\frac{3^{4}-27-64}{2^{8}}}{\frac{4\times 16\times 27\times 3^{-2}}{2^{12}\times 3^{1}}} trí \frac{\frac{\left(3^{7}\times 0.3\right)^{-4}\times 2^{2}}{3^{4}\times 2^{-2}-4^{2}}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}} a mhéadú faoi dheilín \frac{\frac{3^{4}-27-64}{2^{8}}}{\frac{4\times 16\times 27\times 3^{-2}}{2^{12}\times 3^{1}}}.

$$\frac{\frac{\left(3^{7}\times 0.3\right)^{-4}\times 2^{2}}{3^{4}\times 2^{-2}-4^{2}}\times \frac{4\times 16\times 27\times 3^{-2}}{2^{12}\times 3^{1}}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Ríomh cumhacht 3 de 7 agus faigh 2187.

$$\frac{\frac{\left(2187\times 0.3\right)^{-4}\times 2^{2}}{3^{4}\times 2^{-2}-4^{2}}\times \frac{4\times 16\times 27\times 3^{-2}}{2^{12}\times 3^{1}}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Méadaigh 2187 agus 0.3 chun 656.1 a fháil.

$$\frac{\frac{656.1^{-4}\times 2^{2}}{3^{4}\times 2^{-2}-4^{2}}\times \frac{4\times 16\times 27\times 3^{-2}}{2^{12}\times 3^{1}}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Ríomh cumhacht 656.1 de -4 agus faigh \frac{10000}{1853020188851841}.

$$\frac{\frac{\frac{10000}{1853020188851841}\times 2^{2}}{3^{4}\times 2^{-2}-4^{2}}\times \frac{4\times 16\times 27\times 3^{-2}}{2^{12}\times 3^{1}}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Ríomh cumhacht 2 de 2 agus faigh 4.

$$\frac{\frac{\frac{10000}{1853020188851841}\times 4}{3^{4}\times 2^{-2}-4^{2}}\times \frac{4\times 16\times 27\times 3^{-2}}{2^{12}\times 3^{1}}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Méadaigh \frac{10000}{1853020188851841} agus 4 chun \frac{40000}{1853020188851841} a fháil.

$$\frac{\frac{\frac{40000}{1853020188851841}}{3^{4}\times 2^{-2}-4^{2}}\times \frac{4\times 16\times 27\times 3^{-2}}{2^{12}\times 3^{1}}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Ríomh cumhacht 3 de 4 agus faigh 81.

$$\frac{\frac{\frac{40000}{1853020188851841}}{81\times 2^{-2}-4^{2}}\times \frac{4\times 16\times 27\times 3^{-2}}{2^{12}\times 3^{1}}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Ríomh cumhacht 2 de -2 agus faigh \frac{1}{4}.

$$\frac{\frac{\frac{40000}{1853020188851841}}{81\times \frac{1}{4}-4^{2}}\times \frac{4\times 16\times 27\times 3^{-2}}{2^{12}\times 3^{1}}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Méadaigh 81 agus \frac{1}{4} chun \frac{81}{4} a fháil.

$$\frac{\frac{\frac{40000}{1853020188851841}}{\frac{81}{4}-4^{2}}\times \frac{4\times 16\times 27\times 3^{-2}}{2^{12}\times 3^{1}}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Ríomh cumhacht 4 de 2 agus faigh 16.

$$\frac{\frac{\frac{40000}{1853020188851841}}{\frac{81}{4}-16}\times \frac{4\times 16\times 27\times 3^{-2}}{2^{12}\times 3^{1}}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Dealaigh 16 ó \frac{81}{4} chun \frac{17}{4} a fháil.

$$\frac{\frac{\frac{40000}{1853020188851841}}{\frac{17}{4}}\times \frac{4\times 16\times 27\times 3^{-2}}{2^{12}\times 3^{1}}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Roinn \frac{40000}{1853020188851841} faoi \frac{17}{4} trí \frac{40000}{1853020188851841} a mhéadú faoi dheilín \frac{17}{4}.

$$\frac{\frac{40000}{1853020188851841}\times \frac{4}{17}\times \frac{4\times 16\times 27\times 3^{-2}}{2^{12}\times 3^{1}}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Méadaigh \frac{40000}{1853020188851841} agus \frac{4}{17} chun \frac{160000}{31501343210481297} a fháil.

$$\frac{\frac{160000}{31501343210481297}\times \frac{4\times 16\times 27\times 3^{-2}}{2^{12}\times 3^{1}}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Cealaigh 3 mar uimhreoir agus ainmneoir.

$$\frac{\frac{160000}{31501343210481297}\times \frac{4\times 9\times 16\times 3^{-2}}{2^{12}}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Méadaigh 4 agus 9 chun 36 a fháil.

$$\frac{\frac{160000}{31501343210481297}\times \frac{36\times 16\times 3^{-2}}{2^{12}}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Méadaigh 36 agus 16 chun 576 a fháil.

$$\frac{\frac{160000}{31501343210481297}\times \frac{576\times 3^{-2}}{2^{12}}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Ríomh cumhacht 3 de -2 agus faigh \frac{1}{9}.

$$\frac{\frac{160000}{31501343210481297}\times \frac{576\times \frac{1}{9}}{2^{12}}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Méadaigh 576 agus \frac{1}{9} chun 64 a fháil.

$$\frac{\frac{160000}{31501343210481297}\times \frac{64}{2^{12}}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Ríomh cumhacht 2 de 12 agus faigh 4096.

$$\frac{\frac{160000}{31501343210481297}\times \frac{64}{4096}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Laghdaigh an codán \frac{64}{4096} chuig na téarmaí is ísle trí 64 a bhaint agus a chealú.

$$\frac{\frac{160000}{31501343210481297}\times \frac{1}{64}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Méadaigh \frac{160000}{31501343210481297} agus \frac{1}{64} chun \frac{2500}{31501343210481297} a fháil.

$$\frac{\frac{2500}{31501343210481297}}{\frac{\frac{3}{4}\times \left(\frac{2}{3}\right)^{2}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Ríomh cumhacht \frac{2}{3} de 2 agus faigh \frac{4}{9}.

$$\frac{\frac{2500}{31501343210481297}}{\frac{\frac{3}{4}\times \frac{4}{9}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Méadaigh \frac{3}{4} agus \frac{4}{9} chun \frac{1}{3} a fháil.

$$\frac{\frac{2500}{31501343210481297}}{\frac{\frac{1}{3}\times \frac{2}{6}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Laghdaigh an codán \frac{2}{6} chuig na téarmaí is ísle trí 2 a bhaint agus a chealú.

$$\frac{\frac{2500}{31501343210481297}}{\frac{\frac{1}{3}\times \frac{1}{3}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Méadaigh \frac{1}{3} agus \frac{1}{3} chun \frac{1}{9} a fháil.

$$\frac{\frac{2500}{31501343210481297}}{\frac{\frac{1}{9}}{\frac{3^{2}}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Ríomh cumhacht 3 de 2 agus faigh 9.

$$\frac{\frac{2500}{31501343210481297}}{\frac{\frac{1}{9}}{\frac{9}{4}\times 2^{2}\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Ríomh cumhacht 2 de 2 agus faigh 4.

$$\frac{\frac{2500}{31501343210481297}}{\frac{\frac{1}{9}}{\frac{9}{4}\times 4\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Méadaigh \frac{9}{4} agus 4 chun 9 a fháil.

$$\frac{\frac{2500}{31501343210481297}}{\frac{\frac{1}{9}}{9\times \frac{2^{3}}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Ríomh cumhacht 2 de 3 agus faigh 8.

$$\frac{\frac{2500}{31501343210481297}}{\frac{\frac{1}{9}}{9\times \frac{8}{3}}\times \frac{3^{4}-27-64}{2^{8}}}$$

Méadaigh 9 agus \frac{8}{3} chun 24 a fháil.

$$\frac{\frac{2500}{31501343210481297}}{\frac{\frac{1}{9}}{24}\times \frac{3^{4}-27-64}{2^{8}}}$$

Scríobh \frac{\frac{1}{9}}{24} mar chodán aonair.

$$\frac{\frac{2500}{31501343210481297}}{\frac{1}{9\times 24}\times \frac{3^{4}-27-64}{2^{8}}}$$

Méadaigh 9 agus 24 chun 216 a fháil.

$$\frac{\frac{2500}{31501343210481297}}{\frac{1}{216}\times \frac{3^{4}-27-64}{2^{8}}}$$

Ríomh cumhacht 3 de 4 agus faigh 81.

$$\frac{\frac{2500}{31501343210481297}}{\frac{1}{216}\times \frac{81-27-64}{2^{8}}}$$

Dealaigh 27 ó 81 chun 54 a fháil.

$$\frac{\frac{2500}{31501343210481297}}{\frac{1}{216}\times \frac{54-64}{2^{8}}}$$

Dealaigh 64 ó 54 chun -10 a fháil.

$$\frac{\frac{2500}{31501343210481297}}{\frac{1}{216}\times \frac{-10}{2^{8}}}$$

Ríomh cumhacht 2 de 8 agus faigh 256.

$$\frac{\frac{2500}{31501343210481297}}{\frac{1}{216}\times \frac{-10}{256}}$$

Laghdaigh an codán \frac{-10}{256} chuig na téarmaí is ísle trí 2 a bhaint agus a chealú.

$$\frac{\frac{2500}{31501343210481297}}{\frac{1}{216}\left(-\frac{5}{128}\right)}$$

Méadaigh \frac{1}{216} agus -\frac{5}{128} chun -\frac{5}{27648} a fháil.

$$\frac{\frac{2500}{31501343210481297}}{-\frac{5}{27648}}$$

Roinn \frac{2500}{31501343210481297} faoi -\frac{5}{27648} trí \frac{2500}{31501343210481297} a mhéadú faoi dheilín -\frac{5}{27648}.

$$\frac{2500}{31501343210481297}\left(-\frac{27648}{5}\right)$$

Méadaigh \frac{2500}{31501343210481297} agus -\frac{27648}{5} chun -\frac{512000}{1166716415203011} a fháil.

$$-\frac{512000}{1166716415203011}$$

Fachtóirigh

$$-\frac{512000}{1166716415203011} = -4.3883843008321 \times 10^{-10}$$