Solve frac{2.18*10^{-18}(1/3^2-1/7^2)}{3*6.6262*10^-34*10^8}

$$\frac { 2.18 \cdot 10 ^ { - 18 } ( \frac { 1 } { 3 ^ { 2 } } - \frac { 1 } { 7 ^ { 2 } } ) } { 3 \cdot 6.6262 \cdot 10 ^ { - 34 } \cdot 10 ^ { 8 } }$$

Evaluate

$$\frac{43600000000000}{43832313}\approx 994699.960278163$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -34 and 8 to get -26.

$$\frac{2.18\times 10^{-18}\left(\frac{1}{3^{2}}-\frac{1}{7^{2}}\right)}{3\times 6.6262\times 10^{-26}}$$

Calculate 10 to the power of -18 and get \frac{1}{1000000000000000000}.

$$\frac{2.18\times \frac{1}{1000000000000000000}\left(\frac{1}{3^{2}}-\frac{1}{7^{2}}\right)}{3\times 6.6262\times 10^{-26}}$$

Multiply 2.18 and \frac{1}{1000000000000000000} to get \frac{109}{50000000000000000000}.

$$\frac{\frac{109}{50000000000000000000}\left(\frac{1}{3^{2}}-\frac{1}{7^{2}}\right)}{3\times 6.6262\times 10^{-26}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{\frac{109}{50000000000000000000}\left(\frac{1}{9}-\frac{1}{7^{2}}\right)}{3\times 6.6262\times 10^{-26}}$$

Calculate 7 to the power of 2 and get 49.

$$\frac{\frac{109}{50000000000000000000}\left(\frac{1}{9}-\frac{1}{49}\right)}{3\times 6.6262\times 10^{-26}}$$

Subtract \frac{1}{49} from \frac{1}{9} to get \frac{40}{441}.

$$\frac{\frac{109}{50000000000000000000}\times \frac{40}{441}}{3\times 6.6262\times 10^{-26}}$$

Multiply \frac{109}{50000000000000000000} and \frac{40}{441} to get \frac{109}{551250000000000000000}.

$$\frac{\frac{109}{551250000000000000000}}{3\times 6.6262\times 10^{-26}}$$

Multiply 3 and 6.6262 to get 19.8786.

$$\frac{\frac{109}{551250000000000000000}}{19.8786\times 10^{-26}}$$

Calculate 10 to the power of -26 and get \frac{1}{100000000000000000000000000}.

$$\frac{\frac{109}{551250000000000000000}}{19.8786\times \frac{1}{100000000000000000000000000}}$$

Multiply 19.8786 and \frac{1}{100000000000000000000000000} to get \frac{99393}{500000000000000000000000000000}.

$$\frac{\frac{109}{551250000000000000000}}{\frac{99393}{500000000000000000000000000000}}$$

Divide \frac{109}{551250000000000000000} by \frac{99393}{500000000000000000000000000000} by multiplying \frac{109}{551250000000000000000} by the reciprocal of \frac{99393}{500000000000000000000000000000}.

$$\frac{109}{551250000000000000000}\times \frac{500000000000000000000000000000}{99393}$$

Multiply \frac{109}{551250000000000000000} and \frac{500000000000000000000000000000}{99393} to get \frac{43600000000000}{43832313}.

$$\frac{43600000000000}{43832313}$$

Factor

$$\frac{109 \cdot 2 ^ {13} \cdot 5 ^ {11}}{4733 \cdot 3 ^ {3} \cdot 7 ^ {3}} = 994699\frac{42091213}{43832313} = 994699.9602781628$$