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

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

Evaluer

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

Løsningsvejledning

Hvis du vil gange potenser for den samme base, skal du tilføje deres eksponenter. Tilføj -27 og -16 for at få -43.

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

Multiplicer 6 og 62 for at få 372.

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

Multiplicer 372 og 6 for at få 2232.

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

Beregn 10 til potensen af -24, og få \frac{1}{1000000000000000000000000}.

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

Multiplicer 2232 og \frac{1}{1000000000000000000000000} for at få \frac{279}{125000000000000000000000}.

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

Multiplicer 2 og 167 for at få 334.

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

Beregn 10 til potensen af -43, og få \frac{1}{10000000000000000000000000000000000000000000}.

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

Multiplicer 334 og \frac{1}{10000000000000000000000000000000000000000000} for at få \frac{167}{5000000000000000000000000000000000000000000}.

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

Multiplicer \frac{167}{5000000000000000000000000000000000000000000} og 81 for at få \frac{13527}{5000000000000000000000000000000000000000000}.

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

Multiplicer \frac{13527}{5000000000000000000000000000000000000000000} og 9 for at få \frac{121743}{5000000000000000000000000000000000000000000}.

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

Omskriv kvadratroden af inddelings \sqrt{\frac{121743}{5000000000000000000000000000000000000000000}} som opdeling af kvadratiske rødder \frac{\sqrt{121743}}{\sqrt{5000000000000000000000000000000000000000000}}.

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

Faktoriser 121743=27^{2}\times 167. Omskriv kvadratroden af produktet \sqrt{27^{2}\times 167} som produktet af kvadratrødderne \sqrt{27^{2}}\sqrt{167}. Tag kvadratroden af 27^{2}.

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

Faktoriser 5000000000000000000000000000000000000000000=1000000000000000000000^{2}\times 5. Omskriv kvadratroden af produktet \sqrt{1000000000000000000000^{2}\times 5} som produktet af kvadratrødderne \sqrt{1000000000000000000000^{2}}\sqrt{5}. Tag kvadratroden af 1000000000000000000000^{2}.

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

Rationaliser \frac{27\sqrt{167}}{1000000000000000000000\sqrt{5}} ved at multiplicere tælleren og nævneren med \sqrt{5}.

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

Kvadratet på \sqrt{5} er 5.

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

Hvis du vil multiplicere \sqrt{167} og \sqrt{5}, skal du multiplicere tallene under kvadratroden.

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

Multiplicer 1000000000000000000000 og 5 for at få 5000000000000000000000.

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

Divider \frac{279}{125000000000000000000000} med \frac{27\sqrt{835}}{5000000000000000000000} ved at multiplicere \frac{279}{125000000000000000000000} med den reciprokke værdi af \frac{27\sqrt{835}}{5000000000000000000000}.

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

Udlign 9\times 5000000000000000000000 i både tælleren og nævneren.

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

Rationaliser \frac{31}{3\times 25\sqrt{835}} ved at multiplicere tælleren og nævneren med \sqrt{835}.

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

Kvadratet på \sqrt{835} er 835.

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

Multiplicer 3 og 25 for at få 75.

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

Multiplicer 75 og 835 for at få 62625.

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