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

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

I-evaluate

$$\frac{31\sqrt{835}}{62625}\approx 0.01430399$$

Mga Hakbang ng Solution

Para mag-multiply ng mga power na may parehong base, i-add ang mga exponent ng mga ito. I-add ang -27 at -16 para makuha ang -43.

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

I-multiply ang 6 at 62 para makuha ang 372.

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

I-multiply ang 372 at 6 para makuha ang 2232.

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

Kalkulahin ang 10 sa power ng -24 at kunin ang \frac{1}{1000000000000000000000000}.

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

I-multiply ang 2232 at \frac{1}{1000000000000000000000000} para makuha ang \frac{279}{125000000000000000000000}.

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

I-multiply ang 2 at 167 para makuha ang 334.

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

Kalkulahin ang 10 sa power ng -43 at kunin ang \frac{1}{10000000000000000000000000000000000000000000}.

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

I-multiply ang 334 at \frac{1}{10000000000000000000000000000000000000000000} para makuha ang \frac{167}{5000000000000000000000000000000000000000000}.

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

I-multiply ang \frac{167}{5000000000000000000000000000000000000000000} at 81 para makuha ang \frac{13527}{5000000000000000000000000000000000000000000}.

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

I-multiply ang \frac{13527}{5000000000000000000000000000000000000000000} at 9 para makuha ang \frac{121743}{5000000000000000000000000000000000000000000}.

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

I-rewrite ang square root ng division na \sqrt{\frac{121743}{5000000000000000000000000000000000000000000}} bilang division ng mga square root na \frac{\sqrt{121743}}{\sqrt{5000000000000000000000000000000000000000000}}.

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

I-factor out ang 121743=27^{2}\times 167. I-rewrite ang square root ng product na \sqrt{27^{2}\times 167} bilang product ng mga square root na \sqrt{27^{2}}\sqrt{167}. Kunin ang square root ng 27^{2}.

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

I-factor out ang 5000000000000000000000000000000000000000000=1000000000000000000000^{2}\times 5. I-rewrite ang square root ng product na \sqrt{1000000000000000000000^{2}\times 5} bilang product ng mga square root na \sqrt{1000000000000000000000^{2}}\sqrt{5}. Kunin ang square root ng 1000000000000000000000^{2}.

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

I-rationalize ang denominator ng \frac{27\sqrt{167}}{1000000000000000000000\sqrt{5}} sa pamamagitan ng pag-multiply ng numerator at denominator sa \sqrt{5}.

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

Ang square ng \sqrt{5} ay 5.

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

Para i-multiply ang \sqrt{167} at \sqrt{5}, i-multiply ang mga numero sa ilalim ng square root.

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

I-multiply ang 1000000000000000000000 at 5 para makuha ang 5000000000000000000000.

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

I-divide ang \frac{279}{125000000000000000000000} gamit ang \frac{27\sqrt{835}}{5000000000000000000000} sa pamamagitan ng pagmu-multiply sa \frac{279}{125000000000000000000000} gamit ang reciprocal ng \frac{27\sqrt{835}}{5000000000000000000000}.

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

I-cancel out ang 9\times 5000000000000000000000 sa parehong numerator at denominator.

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

I-rationalize ang denominator ng \frac{31}{3\times 25\sqrt{835}} sa pamamagitan ng pag-multiply ng numerator at denominator sa \sqrt{835}.

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

Ang square ng \sqrt{835} ay 835.

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

I-multiply ang 3 at 25 para makuha ang 75.

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

I-multiply ang 75 at 835 para makuha ang 62625.

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