Solve E=frac{9*10^{9}*2(2*10^{-6}*10^{-2})*5*10^{-2}}{[(5*10^{-2})^2-(0.5*10^-2)^2]^2}

$$E = \frac { 9 \times 10 ^ { 9 } \times 2 ( 2 \times 10 ^ { - 6 } \times 10 ^ { - 2 } ) \times 5 \times 10 ^ { - 2 } } { [ ( 5 \times 10 ^ { - 2 } ) ^ { 2 } - ( 0.5 \times 10 ^ { - 2 } ) ^ { 2 } ] ^ { 2 } }$$

Solve for E

$$E = \frac{3200000000}{1089} = 2938475\frac{725}{1089} \approx 2938475.665748393$$

Steps for Solving Linear Equation

To multiply powers of the same base, add their exponents. Add 9 and -6 to get 3.

$$E=\frac{9\times 10^{3}\times 2\times 2\times 10^{-2}\times 5\times 10^{-2}}{\left(\left(5\times 10^{-2}\right)^{2}-\left(0.5\times 10^{-2}\right)^{2}\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 3 and -2 to get 1.

$$E=\frac{9\times 10^{1}\times 2\times 2\times 5\times 10^{-2}}{\left(\left(5\times 10^{-2}\right)^{2}-\left(0.5\times 10^{-2}\right)^{2}\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 1 and -2 to get -1.

$$E=\frac{9\times 10^{-1}\times 2\times 2\times 5}{\left(\left(5\times 10^{-2}\right)^{2}-\left(0.5\times 10^{-2}\right)^{2}\right)^{2}}$$

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

$$E=\frac{9\times \frac{1}{10}\times 2\times 2\times 5}{\left(\left(5\times 10^{-2}\right)^{2}-\left(0.5\times 10^{-2}\right)^{2}\right)^{2}}$$

Multiply 9 and \frac{1}{10} to get \frac{9}{10}.

$$E=\frac{\frac{9}{10}\times 2\times 2\times 5}{\left(\left(5\times 10^{-2}\right)^{2}-\left(0.5\times 10^{-2}\right)^{2}\right)^{2}}$$

Multiply \frac{9}{10} and 2 to get \frac{9}{5}.

$$E=\frac{\frac{9}{5}\times 2\times 5}{\left(\left(5\times 10^{-2}\right)^{2}-\left(0.5\times 10^{-2}\right)^{2}\right)^{2}}$$

Multiply \frac{9}{5} and 2 to get \frac{18}{5}.

$$E=\frac{\frac{18}{5}\times 5}{\left(\left(5\times 10^{-2}\right)^{2}-\left(0.5\times 10^{-2}\right)^{2}\right)^{2}}$$

Multiply \frac{18}{5} and 5 to get 18.

$$E=\frac{18}{\left(\left(5\times 10^{-2}\right)^{2}-\left(0.5\times 10^{-2}\right)^{2}\right)^{2}}$$

Calculate 10 to the power of -2 and get \frac{1}{100}.

$$E=\frac{18}{\left(\left(5\times \frac{1}{100}\right)^{2}-\left(0.5\times 10^{-2}\right)^{2}\right)^{2}}$$

Multiply 5 and \frac{1}{100} to get \frac{1}{20}.

$$E=\frac{18}{\left(\left(\frac{1}{20}\right)^{2}-\left(0.5\times 10^{-2}\right)^{2}\right)^{2}}$$

Calculate \frac{1}{20} to the power of 2 and get \frac{1}{400}.

$$E=\frac{18}{\left(\frac{1}{400}-\left(0.5\times 10^{-2}\right)^{2}\right)^{2}}$$

Calculate 10 to the power of -2 and get \frac{1}{100}.

$$E=\frac{18}{\left(\frac{1}{400}-\left(0.5\times \frac{1}{100}\right)^{2}\right)^{2}}$$

Multiply 0.5 and \frac{1}{100} to get \frac{1}{200}.

$$E=\frac{18}{\left(\frac{1}{400}-\left(\frac{1}{200}\right)^{2}\right)^{2}}$$

Calculate \frac{1}{200} to the power of 2 and get \frac{1}{40000}.

$$E=\frac{18}{\left(\frac{1}{400}-\frac{1}{40000}\right)^{2}}$$

Subtract \frac{1}{40000} from \frac{1}{400} to get \frac{99}{40000}.

$$E=\frac{18}{\left(\frac{99}{40000}\right)^{2}}$$

Calculate \frac{99}{40000} to the power of 2 and get \frac{9801}{1600000000}.

$$E=\frac{18}{\frac{9801}{1600000000}}$$

Divide 18 by \frac{9801}{1600000000} by multiplying 18 by the reciprocal of \frac{9801}{1600000000}.

$$E=18\times \frac{1600000000}{9801}$$

Multiply 18 and \frac{1600000000}{9801} to get \frac{3200000000}{1089}.

$$E=\frac{3200000000}{1089}$$

Assign E

$$E≔\frac{3200000000}{1089}$$