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

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

Evalueren

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

Oplossingsstappen

Als u machten met hetzelfde grondtal wilt vermenigvuldigen, telt u de bijbehorende exponenten bij elkaar op. Tel -31 en -9 op om -40 te krijgen.

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

Bereken 3 tot de macht van 2 en krijg 9.

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

Vermenigvuldig 6 en 626 om 3756 te krijgen.

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

Bereken 10 tot de macht van -34 en krijg \frac{1}{10000000000000000000000000000000000}.

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

Vermenigvuldig 3756 en \frac{1}{10000000000000000000000000000000000} om \frac{939}{2500000000000000000000000000000000} te krijgen.

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

Bereken \frac{939}{2500000000000000000000000000000000} tot de macht van 2 en krijg \frac{881721}{6250000000000000000000000000000000000000000000000000000000000000000}.

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

Vermenigvuldig 9 en \frac{881721}{6250000000000000000000000000000000000000000000000000000000000000000} om \frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000} te krijgen.

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

Vermenigvuldig 8 en 9 om 72 te krijgen.

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

Vermenigvuldig 72 en 1 om 72 te krijgen.

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

Bereken 10 tot de macht van -40 en krijg \frac{1}{10000000000000000000000000000000000000000}.

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

Vermenigvuldig 72 en \frac{1}{10000000000000000000000000000000000000000} om \frac{9}{1250000000000000000000000000000000000000} te krijgen.

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

Vermenigvuldig \frac{9}{1250000000000000000000000000000000000000} en 4805 om \frac{8649}{250000000000000000000000000000000000000} te krijgen.

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

Deel \frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000} door \frac{8649}{250000000000000000000000000000000000000} door \frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000} te vermenigvuldigen met de omgekeerde waarde van \frac{8649}{250000000000000000000000000000000000000}.

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

Vermenigvuldig \frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000} en \frac{250000000000000000000000000000000000000}{8649} om \frac{881721}{24025000000000000000000000000000} te krijgen.

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

Factoriseren

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