Solve 9*10^9((-5*10^-6)(-4*10^-6)/0.2^2)

$$9 \times { 10 }^{ 9 } ( \frac{ (-5 \times { 10 }^{ -6 } )(-4 \times { 10 }^{ -6 } ) }{ { 0.2 }^{ 2 } } )$$

Evaluate

$$4.5$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -6 and -6 to get -12.

$$9\times 10^{9}\times \frac{-5\times 10^{-12}\left(-4\right)}{0.2^{2}}$$

Calculate 10 to the power of 9 and get 1000000000.

$$9\times 1000000000\times \frac{-5\times 10^{-12}\left(-4\right)}{0.2^{2}}$$

Multiply 9 and 1000000000 to get 9000000000.

$$9000000000\times \frac{-5\times 10^{-12}\left(-4\right)}{0.2^{2}}$$

Calculate 10 to the power of -12 and get \frac{1}{1000000000000}.

$$9000000000\times \frac{-5\times \frac{1}{1000000000000}\left(-4\right)}{0.2^{2}}$$

Multiply -5 and \frac{1}{1000000000000} to get -\frac{1}{200000000000}.

$$9000000000\times \frac{-\frac{1}{200000000000}\left(-4\right)}{0.2^{2}}$$

Multiply -\frac{1}{200000000000} and -4 to get \frac{1}{50000000000}.

$$9000000000\times \frac{\frac{1}{50000000000}}{0.2^{2}}$$

Calculate 0.2 to the power of 2 and get 0.04.

$$9000000000\times \frac{\frac{1}{50000000000}}{0.04}$$

Express \frac{\frac{1}{50000000000}}{0.04} as a single fraction.

$$9000000000\times \frac{1}{50000000000\times 0.04}$$

Multiply 50000000000 and 0.04 to get 2000000000.

$$9000000000\times \frac{1}{2000000000}$$

Multiply 9000000000 and \frac{1}{2000000000} to get \frac{9}{2}.

$$\frac{9}{2}$$

Factor

$$\frac{3 ^ {2}}{2} = 4\frac{1}{2} = 4.5$$