Solve frac{4*9.1094*10^{-31}*(3*10^{8})^2*8.8542*10^-2}{(1.6022*10^-19)^2}

$$\frac { 4 \times 9.1094 \times 10 ^ { - 31 } \times ( 3 \times 10 ^ { 8 } ) ^ { 2 } \times 8.8542 \times 10 ^ { - 2 } } { ( 1.6022 \times 10 ^ { - 19 } ) ^ { 2 } }$$

Evaluate

$$\frac{72590804532000000000000000000000}{64176121}\approx 1.131118606 \cdot 10^{24}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -31 and -2 to get -33.

$$\frac{4\times 9.1094\times 10^{-33}\times \left(3\times 10^{8}\right)^{2}\times 8.8542}{\left(1.6022\times 10^{-19}\right)^{2}}$$

Multiply 4 and 9.1094 to get 36.4376.

$$\frac{36.4376\times 10^{-33}\times \left(3\times 10^{8}\right)^{2}\times 8.8542}{\left(1.6022\times 10^{-19}\right)^{2}}$$

Calculate 10 to the power of -33 and get \frac{1}{1000000000000000000000000000000000}.

$$\frac{36.4376\times \frac{1}{1000000000000000000000000000000000}\times \left(3\times 10^{8}\right)^{2}\times 8.8542}{\left(1.6022\times 10^{-19}\right)^{2}}$$

Multiply 36.4376 and \frac{1}{1000000000000000000000000000000000} to get \frac{45547}{1250000000000000000000000000000000000}.

$$\frac{\frac{45547}{1250000000000000000000000000000000000}\times \left(3\times 10^{8}\right)^{2}\times 8.8542}{\left(1.6022\times 10^{-19}\right)^{2}}$$

Calculate 10 to the power of 8 and get 100000000.

$$\frac{\frac{45547}{1250000000000000000000000000000000000}\times \left(3\times 100000000\right)^{2}\times 8.8542}{\left(1.6022\times 10^{-19}\right)^{2}}$$

Multiply 3 and 100000000 to get 300000000.

$$\frac{\frac{45547}{1250000000000000000000000000000000000}\times 300000000^{2}\times 8.8542}{\left(1.6022\times 10^{-19}\right)^{2}}$$

Calculate 300000000 to the power of 2 and get 90000000000000000.

$$\frac{\frac{45547}{1250000000000000000000000000000000000}\times 90000000000000000\times 8.8542}{\left(1.6022\times 10^{-19}\right)^{2}}$$

Multiply \frac{45547}{1250000000000000000000000000000000000} and 90000000000000000 to get \frac{409923}{125000000000000000000}.

$$\frac{\frac{409923}{125000000000000000000}\times 8.8542}{\left(1.6022\times 10^{-19}\right)^{2}}$$

Multiply \frac{409923}{125000000000000000000} and 8.8542 to get \frac{18147701133}{625000000000000000000000}.

$$\frac{\frac{18147701133}{625000000000000000000000}}{\left(1.6022\times 10^{-19}\right)^{2}}$$

Calculate 10 to the power of -19 and get \frac{1}{10000000000000000000}.

$$\frac{\frac{18147701133}{625000000000000000000000}}{\left(1.6022\times \frac{1}{10000000000000000000}\right)^{2}}$$

Multiply 1.6022 and \frac{1}{10000000000000000000} to get \frac{8011}{50000000000000000000000}.

$$\frac{\frac{18147701133}{625000000000000000000000}}{\left(\frac{8011}{50000000000000000000000}\right)^{2}}$$

Calculate \frac{8011}{50000000000000000000000} to the power of 2 and get \frac{64176121}{2500000000000000000000000000000000000000000000}.

$$\frac{\frac{18147701133}{625000000000000000000000}}{\frac{64176121}{2500000000000000000000000000000000000000000000}}$$

Divide \frac{18147701133}{625000000000000000000000} by \frac{64176121}{2500000000000000000000000000000000000000000000} by multiplying \frac{18147701133}{625000000000000000000000} by the reciprocal of \frac{64176121}{2500000000000000000000000000000000000000000000}.

$$\frac{18147701133}{625000000000000000000000}\times \frac{2500000000000000000000000000000000000000000000}{64176121}$$

Multiply \frac{18147701133}{625000000000000000000000} and \frac{2500000000000000000000000000000000000000000000}{64176121} to get \frac{72590804532000000000000000000000}{64176121}.

$$\frac{72590804532000000000000000000000}{64176121}$$

Factor

$$\frac{37 \cdot 1231 \cdot 4919 \cdot 2 ^ {23} \cdot 3 ^ {4} \cdot 5 ^ {21}}{8011 ^ {2}} = 1.1311186061245428 \times 10^{24}\frac{13179916}{64176121} = 1.1311186061245428 \times 10^{24}$$