Solve 9*10^9*2*10^-6*5*10^-6/(0.4)^2

$$9 \times 10 ^ { 9 } \times \frac { 2 \times 10 ^ { - 6 } \times 5 \times 10 ^ { - 6 } } { ( 0.4 ) ^ { 2 } }$$

Evaluate

$$0.5625$$

Solution Steps

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

$$9\times 10^{9}\times \frac{2\times 10^{-12}\times 5}{0.4^{2}}$$

Calculate 10 to the power of 9 and get 1000000000.

$$9\times 1000000000\times \frac{2\times 10^{-12}\times 5}{0.4^{2}}$$

Multiply 9 and 1000000000 to get 9000000000.

$$9000000000\times \frac{2\times 10^{-12}\times 5}{0.4^{2}}$$

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

$$9000000000\times \frac{2\times \frac{1}{1000000000000}\times 5}{0.4^{2}}$$

Multiply 2 and \frac{1}{1000000000000} to get \frac{1}{500000000000}.

$$9000000000\times \frac{\frac{1}{500000000000}\times 5}{0.4^{2}}$$

Multiply \frac{1}{500000000000} and 5 to get \frac{1}{100000000000}.

$$9000000000\times \frac{\frac{1}{100000000000}}{0.4^{2}}$$

Calculate 0.4 to the power of 2 and get 0.16.

$$9000000000\times \frac{\frac{1}{100000000000}}{0.16}$$

Express \frac{\frac{1}{100000000000}}{0.16} as a single fraction.

$$9000000000\times \frac{1}{100000000000\times 0.16}$$

Multiply 100000000000 and 0.16 to get 16000000000.

$$9000000000\times \frac{1}{16000000000}$$

Multiply 9000000000 and \frac{1}{16000000000} to get \frac{9}{16}.

$$\frac{9}{16}$$

Factor

$$\frac{3 ^ {2}}{2 ^ {4}} = 0.5625$$