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

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

Arvuta

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

Lahenduse etapid

Sama alusega astmete korrutamiseks liitke astendajad. Liitke -27 ja -16, et saada -43.

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

Korrutage 6 ja 62, et leida 372.

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

Korrutage 372 ja 6, et leida 2232.

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

Arvutage -24 aste 10 ja leidke \frac{1}{1000000000000000000000000}.

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

Korrutage 2232 ja \frac{1}{1000000000000000000000000}, et leida \frac{279}{125000000000000000000000}.

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

Korrutage 2 ja 167, et leida 334.

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

Arvutage -43 aste 10 ja leidke \frac{1}{10000000000000000000000000000000000000000000}.

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

Korrutage 334 ja \frac{1}{10000000000000000000000000000000000000000000}, et leida \frac{167}{5000000000000000000000000000000000000000000}.

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

Korrutage \frac{167}{5000000000000000000000000000000000000000000} ja 81, et leida \frac{13527}{5000000000000000000000000000000000000000000}.

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

Korrutage \frac{13527}{5000000000000000000000000000000000000000000} ja 9, et leida \frac{121743}{5000000000000000000000000000000000000000000}.

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

Kirjutage: allüksus \sqrt{\frac{121743}{5000000000000000000000000000000000000000000}}: allüksus juured \frac{\sqrt{121743}}{\sqrt{5000000000000000000000000000000000000000000}}.

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

Tegurda 121743=27^{2}\times 167. Kirjutage \sqrt{27^{2}\times 167} toote juured, kui see ruut \sqrt{27^{2}}\sqrt{167}. Leidke 27^{2} ruutjuur.

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

Tegurda 5000000000000000000000000000000000000000000=1000000000000000000000^{2}\times 5. Kirjutage \sqrt{1000000000000000000000^{2}\times 5} toote juured, kui see ruut \sqrt{1000000000000000000000^{2}}\sqrt{5}. Leidke 1000000000000000000000^{2} ruutjuur.

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

Ratsionaliseerige korrutades lugeja ja \sqrt{5} nimetaja \frac{27\sqrt{167}}{1000000000000000000000\sqrt{5}} nimetaja.

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

\sqrt{5} ruut on 5.

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

\sqrt{167} ja \sqrt{5} korrutage numbrid, mis on sama juur.

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

Korrutage 1000000000000000000000 ja 5, et leida 5000000000000000000000.

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

Jagage \frac{279}{125000000000000000000000} väärtusega \frac{27\sqrt{835}}{5000000000000000000000}, korrutades \frac{279}{125000000000000000000000} väärtuse \frac{27\sqrt{835}}{5000000000000000000000} pöördväärtusega.

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

Taandage 9\times 5000000000000000000000 nii lugejas kui ka nimetajas.

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

Ratsionaliseerige korrutades lugeja ja \sqrt{835} nimetaja \frac{31}{3\times 25\sqrt{835}} nimetaja.

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

\sqrt{835} ruut on 835.

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

Korrutage 3 ja 25, et leida 75.

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

Korrutage 75 ja 835, et leida 62625.

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