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

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

Evalwa

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

Passi tas-Soluzzjonijiet

Biex timmultiplika l-qawwa tal-istess bażi, żid l-esponenti tagħhom. Żid -27 u -16 biex tikseb -43.

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

Immultiplika 6 u 62 biex tikseb 372.

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

Immultiplika 372 u 6 biex tikseb 2232.

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

Ikkalkula 10 bil-power ta' -24 u tikseb \frac{1}{1000000000000000000000000}.

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

Immultiplika 2232 u \frac{1}{1000000000000000000000000} biex tikseb \frac{279}{125000000000000000000000}.

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

Immultiplika 2 u 167 biex tikseb 334.

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

Ikkalkula 10 bil-power ta' -43 u tikseb \frac{1}{10000000000000000000000000000000000000000000}.

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

Immultiplika 334 u \frac{1}{10000000000000000000000000000000000000000000} biex tikseb \frac{167}{5000000000000000000000000000000000000000000}.

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

Immultiplika \frac{167}{5000000000000000000000000000000000000000000} u 81 biex tikseb \frac{13527}{5000000000000000000000000000000000000000000}.

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

Immultiplika \frac{13527}{5000000000000000000000000000000000000000000} u 9 biex tikseb \frac{121743}{5000000000000000000000000000000000000000000}.

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

Erġa' ikteb id-diviżjoni tal-għerq kwadrat \sqrt{\frac{121743}{5000000000000000000000000000000000000000000}} bħala d-diviżjoni tal-għeruq kwadrati \frac{\sqrt{121743}}{\sqrt{5000000000000000000000000000000000000000000}}.

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

Iffattura 121743=27^{2}\times 167. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{27^{2}\times 167} bħala l-prodott tal-għeruq kwadrati \sqrt{27^{2}}\sqrt{167}. Ħu l-għerq kwadrat ta' 27^{2}.

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

Iffattura 5000000000000000000000000000000000000000000=1000000000000000000000^{2}\times 5. Erġa' ikteb l-għerq kwadrat tal-prodott \sqrt{1000000000000000000000^{2}\times 5} bħala l-prodott tal-għeruq kwadrati \sqrt{1000000000000000000000^{2}}\sqrt{5}. Ħu l-għerq kwadrat ta' 1000000000000000000000^{2}.

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

Irrazzjonalizza d-denominatur tal-\frac{27\sqrt{167}}{1000000000000000000000\sqrt{5}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{5}.

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

Il-kwadrat ta' \sqrt{5} huwa 5.

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

Biex timmultiplika \sqrt{167} u \sqrt{5}, immultiplika n-numri taħt l-għerq kwadrat.

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

Immultiplika 1000000000000000000000 u 5 biex tikseb 5000000000000000000000.

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

Iddividi \frac{279}{125000000000000000000000} b'\frac{27\sqrt{835}}{5000000000000000000000} billi timmultiplika \frac{279}{125000000000000000000000} bir-reċiproku ta' \frac{27\sqrt{835}}{5000000000000000000000}.

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

Annulla 9\times 5000000000000000000000 fin-numeratur u d-denominatur.

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

Irrazzjonalizza d-denominatur tal-\frac{31}{3\times 25\sqrt{835}} billi timmultiplika in-numeratur u d-denominatur mill-\sqrt{835}.

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

Il-kwadrat ta' \sqrt{835} huwa 835.

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

Immultiplika 3 u 25 biex tikseb 75.

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

Immultiplika 75 u 835 biex tikseb 62625.

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