Solve =3(9*10^9)(12*10^-6)^2/4(0.16)^2

$$= \frac { 3 ( 9 * 10 ^ { 9 } ) ( 12 * 10 ^ { - 6 } ) ^ { 2 } } { 4 ( 0.16 ) ^ { 2 } }$$

Evaluate

$$37.96875$$

Solution Steps

Multiply 3 and 9 to get 27.

$$\frac{27\times 10^{9}\times \left(12\times 10^{-6}\right)^{2}}{4\times 0.16^{2}}$$

Calculate 10 to the power of 9 and get 1000000000.

$$\frac{27\times 1000000000\times \left(12\times 10^{-6}\right)^{2}}{4\times 0.16^{2}}$$

Multiply 27 and 1000000000 to get 27000000000.

$$\frac{27000000000\times \left(12\times 10^{-6}\right)^{2}}{4\times 0.16^{2}}$$

Calculate 10 to the power of -6 and get \frac{1}{1000000}.

$$\frac{27000000000\times \left(12\times \frac{1}{1000000}\right)^{2}}{4\times 0.16^{2}}$$

Multiply 12 and \frac{1}{1000000} to get \frac{3}{250000}.

$$\frac{27000000000\times \left(\frac{3}{250000}\right)^{2}}{4\times 0.16^{2}}$$

Calculate \frac{3}{250000} to the power of 2 and get \frac{9}{62500000000}.

$$\frac{27000000000\times \frac{9}{62500000000}}{4\times 0.16^{2}}$$

Multiply 27000000000 and \frac{9}{62500000000} to get \frac{486}{125}.

$$\frac{\frac{486}{125}}{4\times 0.16^{2}}$$

Calculate 0.16 to the power of 2 and get 0.0256.

$$\frac{\frac{486}{125}}{4\times 0.0256}$$

Multiply 4 and 0.0256 to get 0.1024.

$$\frac{\frac{486}{125}}{0.1024}$$

Express \frac{\frac{486}{125}}{0.1024} as a single fraction.

$$\frac{486}{125\times 0.1024}$$

Multiply 125 and 0.1024 to get 12.8.

$$\frac{486}{12.8}$$

Expand \frac{486}{12.8} by multiplying both numerator and the denominator by 10.

$$\frac{4860}{128}$$

Reduce the fraction \frac{4860}{128} to lowest terms by extracting and canceling out 4.

$$\frac{1215}{32}$$

Factor

$$\frac{5 \cdot 3 ^ {5}}{2 ^ {5}} = 37\frac{31}{32} = 37.96875$$