Solve frac{3^{2}*(6*626*10^-34)^2}{8*9*1*10^-31*(48.05*10^-9)}

$$\frac { 3 ^ { 2 } \times ( 6 \cdot 626 \times 10 ^ { - 34 } ) ^ { 2 } } { 8 \times 9 \cdot 1 \times 10 ^ { - 31 } \times ( 48.05 \times 10 ^ { - 9 } ) }$$

Evaluate

$$\frac{881721}{240250000000000000000000000000}\approx 3.670014568 \cdot 10^{-24}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -31 and -9 to get -40.

$$\frac{3^{2}\times \left(6\times 626\times 10^{-34}\right)^{2}}{8\times 9\times 1\times 10^{-40}\times 48.05}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9\times \left(6\times 626\times 10^{-34}\right)^{2}}{8\times 9\times 1\times 10^{-40}\times 48.05}$$

Multiply 6 and 626 to get 3756.

$$\frac{9\times \left(3756\times 10^{-34}\right)^{2}}{8\times 9\times 1\times 10^{-40}\times 48.05}$$

Calculate 10 to the power of -34 and get \frac{1}{10000000000000000000000000000000000}.

$$\frac{9\times \left(3756\times \frac{1}{10000000000000000000000000000000000}\right)^{2}}{8\times 9\times 1\times 10^{-40}\times 48.05}$$

Multiply 3756 and \frac{1}{10000000000000000000000000000000000} to get \frac{939}{2500000000000000000000000000000000}.

$$\frac{9\times \left(\frac{939}{2500000000000000000000000000000000}\right)^{2}}{8\times 9\times 1\times 10^{-40}\times 48.05}$$

Calculate \frac{939}{2500000000000000000000000000000000} to the power of 2 and get \frac{881721}{6250000000000000000000000000000000000000000000000000000000000000000}.

$$\frac{9\times \frac{881721}{6250000000000000000000000000000000000000000000000000000000000000000}}{8\times 9\times 1\times 10^{-40}\times 48.05}$$

Multiply 9 and \frac{881721}{6250000000000000000000000000000000000000000000000000000000000000000} to get \frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000}.

$$\frac{\frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000}}{8\times 9\times 1\times 10^{-40}\times 48.05}$$

Multiply 8 and 9 to get 72.

$$\frac{\frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000}}{72\times 1\times 10^{-40}\times 48.05}$$

Multiply 72 and 1 to get 72.

$$\frac{\frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000}}{72\times 10^{-40}\times 48.05}$$

Calculate 10 to the power of -40 and get \frac{1}{10000000000000000000000000000000000000000}.

$$\frac{\frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000}}{72\times \frac{1}{10000000000000000000000000000000000000000}\times 48.05}$$

Multiply 72 and \frac{1}{10000000000000000000000000000000000000000} to get \frac{9}{1250000000000000000000000000000000000000}.

$$\frac{\frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000}}{\frac{9}{1250000000000000000000000000000000000000}\times 48.05}$$

Multiply \frac{9}{1250000000000000000000000000000000000000} and 48.05 to get \frac{8649}{25000000000000000000000000000000000000000}.

$$\frac{\frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000}}{\frac{8649}{25000000000000000000000000000000000000000}}$$

Divide \frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000} by \frac{8649}{25000000000000000000000000000000000000000} by multiplying \frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000} by the reciprocal of \frac{8649}{25000000000000000000000000000000000000000}.

$$\frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000}\times \frac{25000000000000000000000000000000000000000}{8649}$$

Multiply \frac{7935489}{6250000000000000000000000000000000000000000000000000000000000000000} and \frac{25000000000000000000000000000000000000000}{8649} to get \frac{881721}{240250000000000000000000000000}.

$$\frac{881721}{240250000000000000000000000000}$$

Factor

$$\frac{3 ^ {2} \cdot 313 ^ {2}}{2 ^ {25} \cdot 5 ^ {27} \cdot 31 ^ {2}} = 3.670014568158169 \times 10^{-24}$$