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

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

Ovrednoti

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

Koraki rešitve

Če želite pomnožiti potence z isto osnovo, seštejte njihove eksponente. Seštejte -27 in -16, da dobite -43.

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

Pomnožite 6 in 62, da dobite 372.

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

Pomnožite 372 in 6, da dobite 2232.

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

Izračunajte potenco 10 števila -24, da dobite \frac{1}{1000000000000000000000000}.

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

Pomnožite 2232 in \frac{1}{1000000000000000000000000}, da dobite \frac{279}{125000000000000000000000}.

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

Pomnožite 2 in 167, da dobite 334.

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

Izračunajte potenco 10 števila -43, da dobite \frac{1}{10000000000000000000000000000000000000000000}.

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

Pomnožite 334 in \frac{1}{10000000000000000000000000000000000000000000}, da dobite \frac{167}{5000000000000000000000000000000000000000000}.

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

Pomnožite \frac{167}{5000000000000000000000000000000000000000000} in 81, da dobite \frac{13527}{5000000000000000000000000000000000000000000}.

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

Pomnožite \frac{13527}{5000000000000000000000000000000000000000000} in 9, da dobite \frac{121743}{5000000000000000000000000000000000000000000}.

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

Znova napišite kvadratni koren deljenja \sqrt{\frac{121743}{5000000000000000000000000000000000000000000}} kot deljenje kvadratnih korenov \frac{\sqrt{121743}}{\sqrt{5000000000000000000000000000000000000000000}}.

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

Faktorizirajte 121743=27^{2}\times 167. Znova napišite kvadratni koren izdelka \sqrt{27^{2}\times 167} kot produkt kvadratnih korenov \sqrt{27^{2}}\sqrt{167}. Uporabite kvadratni koren števila 27^{2}.

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

Faktorizirajte 5000000000000000000000000000000000000000000=1000000000000000000000^{2}\times 5. Znova napišite kvadratni koren izdelka \sqrt{1000000000000000000000^{2}\times 5} kot produkt kvadratnih korenov \sqrt{1000000000000000000000^{2}}\sqrt{5}. Uporabite kvadratni koren števila 1000000000000000000000^{2}.

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

Racionalizirajte imenovalec \frac{27\sqrt{167}}{1000000000000000000000\sqrt{5}} tako, da pomnožite števec in imenovalec s \sqrt{5}.

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

Kvadrat vrednosti \sqrt{5} je 5.

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

Če želite \sqrt{167} pomnožite in \sqrt{5}, pomnožite številke v kvadratni korenu.

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

Pomnožite 1000000000000000000000 in 5, da dobite 5000000000000000000000.

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

Delite \frac{279}{125000000000000000000000} s/z \frac{27\sqrt{835}}{5000000000000000000000} tako, da pomnožite \frac{279}{125000000000000000000000} z obratno vrednostjo \frac{27\sqrt{835}}{5000000000000000000000}.

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

Okrajšaj 9\times 5000000000000000000000 v števcu in imenovalcu.

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

Racionalizirajte imenovalec \frac{31}{3\times 25\sqrt{835}} tako, da pomnožite števec in imenovalec s \sqrt{835}.

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

Kvadrat vrednosti \sqrt{835} je 835.

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

Pomnožite 3 in 25, da dobite 75.

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

Pomnožite 75 in 835, da dobite 62625.

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