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

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

Procijeni

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

Koraci za rješenje

Da biste pomnožili stepene iste osnove, saberite eksponente. Saberite -27 i -16 da biste dobili -43.

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

Pomnožite 6 i 62 da biste dobili 372.

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

Pomnožite 372 i 6 da biste dobili 2232.

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

Izračunajte 10 stepen od -24 i dobijte \frac{1}{1000000000000000000000000}.

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

Pomnožite 2232 i \frac{1}{1000000000000000000000000} da biste dobili \frac{279}{125000000000000000000000}.

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

Pomnožite 2 i 167 da biste dobili 334.

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

Izračunajte 10 stepen od -43 i dobijte \frac{1}{10000000000000000000000000000000000000000000}.

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

Pomnožite 334 i \frac{1}{10000000000000000000000000000000000000000000} da biste dobili \frac{167}{5000000000000000000000000000000000000000000}.

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

Pomnožite \frac{167}{5000000000000000000000000000000000000000000} i 81 da biste dobili \frac{13527}{5000000000000000000000000000000000000000000}.

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

Pomnožite \frac{13527}{5000000000000000000000000000000000000000000} i 9 da biste dobili \frac{121743}{5000000000000000000000000000000000000000000}.

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

Ponovo napišite kvadratni korijen dijeljenja \sqrt{\frac{121743}{5000000000000000000000000000000000000000000}} kao dijeljenje kvadratnih korijena \frac{\sqrt{121743}}{\sqrt{5000000000000000000000000000000000000000000}}.

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

Faktorirajte 121743=27^{2}\times 167. Ponovo napišite kvadratni korijen proizvoda \sqrt{27^{2}\times 167} kao proizvod kvadratnih korijena \sqrt{27^{2}}\sqrt{167}. Izračunajte kvadratni korijen od 27^{2}.

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

Faktorirajte 5000000000000000000000000000000000000000000=1000000000000000000000^{2}\times 5. Ponovo napišite kvadratni korijen proizvoda \sqrt{1000000000000000000000^{2}\times 5} kao proizvod kvadratnih korijena \sqrt{1000000000000000000000^{2}}\sqrt{5}. Izračunajte kvadratni korijen od 1000000000000000000000^{2}.

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

Racionalizirajte imenilac broja \frac{27\sqrt{167}}{1000000000000000000000\sqrt{5}} tako što ćete pomnožiti brojilac i imenilac sa \sqrt{5}.

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

Kvadrat broja \sqrt{5} je 5.

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

Da biste pomnožili \sqrt{167} i \sqrt{5}, pomnožite brojeve u okviru kvadratnog korijena.

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

Pomnožite 1000000000000000000000 i 5 da biste dobili 5000000000000000000000.

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

Podijelite \frac{279}{125000000000000000000000} sa \frac{27\sqrt{835}}{5000000000000000000000} tako što ćete pomnožiti \frac{279}{125000000000000000000000} recipročnom vrijednošću od \frac{27\sqrt{835}}{5000000000000000000000}.

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

Otkaži 9\times 5000000000000000000000 u brojiocu i imeniocu.

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

Racionalizirajte imenilac broja \frac{31}{3\times 25\sqrt{835}} tako što ćete pomnožiti brojilac i imenilac sa \sqrt{835}.

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

Kvadrat broja \sqrt{835} je 835.

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

Pomnožite 3 i 25 da biste dobili 75.

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

Pomnožite 75 i 835 da biste dobili 62625.

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