Solve =8.99*10^{9}(73.6*10^-19*73.6*10^-19/2*(5.9*10^-15)^2)

$$= 8.99 \times 10 ^ { 9 } ( \frac { 73.6 \times 10 ^ { - 19 } \times 73.6 \times 10 ^ { - 19 } } { 2 \times ( 5.9 \times 10 ^ { - 15 } ) ^ { 2 } } )$$

Evaluate

$$\frac{121746176}{17405}\approx 6994.896638897$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -19 and -19 to get -38.

$$8.99\times 10^{9}\times \frac{73.6\times 10^{-38}\times 73.6}{2\times \left(5.9\times 10^{-15}\right)^{2}}$$

Calculate 10 to the power of 9 and get 1000000000.

$$8.99\times 1000000000\times \frac{73.6\times 10^{-38}\times 73.6}{2\times \left(5.9\times 10^{-15}\right)^{2}}$$

Multiply 8.99 and 1000000000 to get 8990000000.

$$8990000000\times \frac{73.6\times 10^{-38}\times 73.6}{2\times \left(5.9\times 10^{-15}\right)^{2}}$$

Calculate 10 to the power of -38 and get \frac{1}{100000000000000000000000000000000000000}.

$$8990000000\times \frac{73.6\times \frac{1}{100000000000000000000000000000000000000}\times 73.6}{2\times \left(5.9\times 10^{-15}\right)^{2}}$$

Multiply 73.6 and \frac{1}{100000000000000000000000000000000000000} to get \frac{23}{31250000000000000000000000000000000000}.

$$8990000000\times \frac{\frac{23}{31250000000000000000000000000000000000}\times 73.6}{2\times \left(5.9\times 10^{-15}\right)^{2}}$$

Multiply \frac{23}{31250000000000000000000000000000000000} and 73.6 to get \frac{529}{9765625000000000000000000000000000000}.

$$8990000000\times \frac{\frac{529}{9765625000000000000000000000000000000}}{2\times \left(5.9\times 10^{-15}\right)^{2}}$$

Calculate 10 to the power of -15 and get \frac{1}{1000000000000000}.

$$8990000000\times \frac{\frac{529}{9765625000000000000000000000000000000}}{2\times \left(5.9\times \frac{1}{1000000000000000}\right)^{2}}$$

Multiply 5.9 and \frac{1}{1000000000000000} to get \frac{59}{10000000000000000}.

$$8990000000\times \frac{\frac{529}{9765625000000000000000000000000000000}}{2\times \left(\frac{59}{10000000000000000}\right)^{2}}$$

Calculate \frac{59}{10000000000000000} to the power of 2 and get \frac{3481}{100000000000000000000000000000000}.

$$8990000000\times \frac{\frac{529}{9765625000000000000000000000000000000}}{2\times \frac{3481}{100000000000000000000000000000000}}$$

Multiply 2 and \frac{3481}{100000000000000000000000000000000} to get \frac{3481}{50000000000000000000000000000000}.

$$8990000000\times \frac{\frac{529}{9765625000000000000000000000000000000}}{\frac{3481}{50000000000000000000000000000000}}$$

Divide \frac{529}{9765625000000000000000000000000000000} by \frac{3481}{50000000000000000000000000000000} by multiplying \frac{529}{9765625000000000000000000000000000000} by the reciprocal of \frac{3481}{50000000000000000000000000000000}.

$$8990000000\times \frac{529}{9765625000000000000000000000000000000}\times \frac{50000000000000000000000000000000}{3481}$$

Multiply \frac{529}{9765625000000000000000000000000000000} and \frac{50000000000000000000000000000000}{3481} to get \frac{1058}{1359765625}.

$$8990000000\times \frac{1058}{1359765625}$$

Multiply 8990000000 and \frac{1058}{1359765625} to get \frac{121746176}{17405}.

$$\frac{121746176}{17405}$$

Factor

$$\frac{29 \cdot 31 \cdot 2 ^ {8} \cdot 23 ^ {2}}{5 \cdot 59 ^ {2}} = 6994\frac{15606}{17405} = 6994.896638896868$$