Resol 6*62*6*10^-24/sqrt{2*167*10^-27*81*9*10^-16}

$$\frac { 6 \cdot 62 \cdot 6 \times 10 ^ { - 24 } } { \sqrt { 2 \times 167 \times 10 ^ { - 27 } \times 81 \cdot 9 \times 10 ^ { - 16 } } }$$

Calcula

$$\frac{31\sqrt{835}}{62625}\approx 0,01430399$$

Passos de solució

Per multiplicar potències de la mateixa base, afegiu-ne els exponents. Afegiu -27 i -16 per obtenir -43.

$$\frac{6\times 62\times 6\times 10^{-24}}{\sqrt{2\times 167\times 10^{-43}\times 81\times 9}}$$

Multipliqueu 6 per 62 per obtenir 372.

$$\frac{372\times 6\times 10^{-24}}{\sqrt{2\times 167\times 10^{-43}\times 81\times 9}}$$

Multipliqueu 372 per 6 per obtenir 2232.

$$\frac{2232\times 10^{-24}}{\sqrt{2\times 167\times 10^{-43}\times 81\times 9}}$$

Calculeu 10 elevat a -24 per obtenir \frac{1}{1000000000000000000000000}.

$$\frac{2232\times \frac{1}{1000000000000000000000000}}{\sqrt{2\times 167\times 10^{-43}\times 81\times 9}}$$

Multipliqueu 2232 per \frac{1}{1000000000000000000000000} per obtenir \frac{279}{125000000000000000000000}.

$$\frac{\frac{279}{125000000000000000000000}}{\sqrt{2\times 167\times 10^{-43}\times 81\times 9}}$$

Multipliqueu 2 per 167 per obtenir 334.

$$\frac{\frac{279}{125000000000000000000000}}{\sqrt{334\times 10^{-43}\times 81\times 9}}$$

Calculeu 10 elevat a -43 per obtenir \frac{1}{10000000000000000000000000000000000000000000}.

$$\frac{\frac{279}{125000000000000000000000}}{\sqrt{334\times \frac{1}{10000000000000000000000000000000000000000000}\times 81\times 9}}$$

Multipliqueu 334 per \frac{1}{10000000000000000000000000000000000000000000} per obtenir \frac{167}{5000000000000000000000000000000000000000000}.

$$\frac{\frac{279}{125000000000000000000000}}{\sqrt{\frac{167}{5000000000000000000000000000000000000000000}\times 81\times 9}}$$

Multipliqueu \frac{167}{5000000000000000000000000000000000000000000} per 81 per obtenir \frac{13527}{5000000000000000000000000000000000000000000}.

$$\frac{\frac{279}{125000000000000000000000}}{\sqrt{\frac{13527}{5000000000000000000000000000000000000000000}\times 9}}$$

Multipliqueu \frac{13527}{5000000000000000000000000000000000000000000} per 9 per obtenir \frac{121743}{5000000000000000000000000000000000000000000}.

$$\frac{\frac{279}{125000000000000000000000}}{\sqrt{\frac{121743}{5000000000000000000000000000000000000000000}}}$$

Torneu a escriure l'arrel quadrada de la divisió \sqrt{\frac{121743}{5000000000000000000000000000000000000000000}} com a divisió d'arrels quadrades \frac{\sqrt{121743}}{\sqrt{5000000000000000000000000000000000000000000}}.

$$\frac{\frac{279}{125000000000000000000000}}{\frac{\sqrt{121743}}{\sqrt{5000000000000000000000000000000000000000000}}}$$

Aïlleu la 121743=27^{2}\times 167. Torna a escriure l'arrel quadrada del producte \sqrt{27^{2}\times 167} com a producte d'arrel quadrada \sqrt{27^{2}}\sqrt{167}. Calculeu l'arrel quadrada de 27^{2}.

$$\frac{\frac{279}{125000000000000000000000}}{\frac{27\sqrt{167}}{\sqrt{5000000000000000000000000000000000000000000}}}$$

Aïlleu la 5000000000000000000000000000000000000000000=1000000000000000000000^{2}\times 5. Torna a escriure l'arrel quadrada del producte \sqrt{1000000000000000000000^{2}\times 5} com a producte d'arrel quadrada \sqrt{1000000000000000000000^{2}}\sqrt{5}. Calculeu l'arrel quadrada de 1000000000000000000000^{2}.

$$\frac{\frac{279}{125000000000000000000000}}{\frac{27\sqrt{167}}{1000000000000000000000\sqrt{5}}}$$

Racionalitzeu el denominador de \frac{27\sqrt{167}}{1000000000000000000000\sqrt{5}} multiplicant el numerador i el denominador per \sqrt{5}.

$$\frac{\frac{279}{125000000000000000000000}}{\frac{27\sqrt{167}\sqrt{5}}{1000000000000000000000\left(\sqrt{5}\right)^{2}}}$$

L'arrel quadrada de \sqrt{5} és 5.

$$\frac{\frac{279}{125000000000000000000000}}{\frac{27\sqrt{167}\sqrt{5}}{1000000000000000000000\times 5}}$$

Per multiplicar \sqrt{167} i \sqrt{5}, Multipliqueu els números sota l'arrel quadrada.

$$\frac{\frac{279}{125000000000000000000000}}{\frac{27\sqrt{835}}{1000000000000000000000\times 5}}$$

Multipliqueu 1000000000000000000000 per 5 per obtenir 5000000000000000000000.

$$\frac{\frac{279}{125000000000000000000000}}{\frac{27\sqrt{835}}{5000000000000000000000}}$$

Dividiu \frac{279}{125000000000000000000000} per \frac{27\sqrt{835}}{5000000000000000000000} multiplicant \frac{279}{125000000000000000000000} pel recíproc de \frac{27\sqrt{835}}{5000000000000000000000}.

$$\frac{279\times 5000000000000000000000}{125000000000000000000000\times 27\sqrt{835}}$$

Anul·leu 9\times 5000000000000000000000 tant al numerador com al denominador.

$$\frac{31}{3\times 25\sqrt{835}}$$

Racionalitzeu el denominador de \frac{31}{3\times 25\sqrt{835}} multiplicant el numerador i el denominador per \sqrt{835}.

$$\frac{31\sqrt{835}}{3\times 25\left(\sqrt{835}\right)^{2}}$$

L'arrel quadrada de \sqrt{835} és 835.

$$\frac{31\sqrt{835}}{3\times 25\times 835}$$

Multipliqueu 3 per 25 per obtenir 75.

$$\frac{31\sqrt{835}}{75\times 835}$$

Multipliqueu 75 per 835 per obtenir 62625.

$$\frac{31\sqrt{835}}{62625}$$