Ratkaise frac{3^{2}*(6*626*10^-34)^2}{8*9*1*10^-31*(4805*10^-9)}

$$\frac { 3 ^ { 2 } \times ( 6 \cdot 626 \times 10 ^ { - 34 } ) ^ { 2 } } { 8 \times 9 \cdot 1 \times 10 ^ { - 31 } \times ( 4805 \times 10 ^ { - 9 } ) }$$

Laske

$$\frac{881721}{24025000000000000000000000000000}\approx 3,670014568 \cdot 10^{-26}$$

Ratkaisun vaiheet

Jos haluat kertoa samankantaiset potenssit, lisää niiden eksponentit yhteen. Lisää -31 ja -9 yhteen saadaksesi -40.

$$\frac{3^{2}\times \left(6\times 626\times 10^{-34}\right)^{2}}{8\times 9\times 1\times 10^{-40}\times 4805}$$

Laske 3 potenssiin 2, jolloin ratkaisuksi tulee 9.

$$\frac{9\times \left(6\times 626\times 10^{-34}\right)^{2}}{8\times 9\times 1\times 10^{-40}\times 4805}$$

Kerro 6 ja 626, niin saadaan 3756.

$$\frac{9\times \left(3756\times 10^{-34}\right)^{2}}{8\times 9\times 1\times 10^{-40}\times 4805}$$

Laske 10 potenssiin -34, jolloin ratkaisuksi tulee \frac{1}{10000000000000000000000000000000000}.

$$\frac{9\times \left(3756\times \frac{1}{10000000000000000000000000000000000}\right)^{2}}{8\times 9\times 1\times 10^{-40}\times 4805}$$

Kerro 3756 ja \frac{1}{10000000000000000000000000000000000}, niin saadaan \frac{939}{2500000000000000000000000000000000}.

$$\frac{9\times \left(\frac{939}{2500000000000000000000000000000000}\right)^{2}}{8\times 9\times 1\times 10^{-40}\times 4805}$$

Laske \frac{939}{2500000000000000000000000000000000} potenssiin 2, jolloin ratkaisuksi tulee \frac{881721}{6250000000000000000000000000000000000000000000000000000000000000000}.

$$\frac{9\times \frac{881721}{6250000000000000000000000000000000000000000000000000000000000000000}}{8\times 9\times 1\times 10^{-40}\times 4805}$$

Kerro 9 ja \frac{881721}{6250000000000000000000000000000000000000000000000000000000000000000}, niin saadaan \frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000}.

$$\frac{\frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000}}{8\times 9\times 1\times 10^{-40}\times 4805}$$

Kerro 8 ja 9, niin saadaan 72.

$$\frac{\frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000}}{72\times 1\times 10^{-40}\times 4805}$$

Kerro 72 ja 1, niin saadaan 72.

$$\frac{\frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000}}{72\times 10^{-40}\times 4805}$$

Laske 10 potenssiin -40, jolloin ratkaisuksi tulee \frac{1}{10000000000000000000000000000000000000000}.

$$\frac{\frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000}}{72\times \frac{1}{10000000000000000000000000000000000000000}\times 4805}$$

Kerro 72 ja \frac{1}{10000000000000000000000000000000000000000}, niin saadaan \frac{9}{1250000000000000000000000000000000000000}.

$$\frac{\frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000}}{\frac{9}{1250000000000000000000000000000000000000}\times 4805}$$

Kerro \frac{9}{1250000000000000000000000000000000000000} ja 4805, niin saadaan \frac{8649}{250000000000000000000000000000000000000}.

$$\frac{\frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000}}{\frac{8649}{250000000000000000000000000000000000000}}$$

Jaa \frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000} luvulla \frac{8649}{250000000000000000000000000000000000000} kertomalla \frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000} luvun \frac{8649}{250000000000000000000000000000000000000} käänteisluvulla.

$$\frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000}\times \frac{250000000000000000000000000000000000000}{8649}$$

Kerro \frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000} ja \frac{250000000000000000000000000000000000000}{8649}, niin saadaan \frac{881721}{24025000000000000000000000000000}.

$$\frac{881721}{24025000000000000000000000000000}$$

Jaa tekijöihin

$$\frac{3 ^ {2} \cdot 313 ^ {2}}{2 ^ {27} \cdot 5 ^ {29} \cdot 31 ^ {2}} = 3,6700145681581686 \times 10^{-26}$$