Solve 9*10^-9(8*10^-9-6*10^-9/frac{0.05^2{{2}^2}}

$$\frac{ 9 \times { 10 }^{ -9 } (8 \times { 10 }^{ -9 } -6 \times { 10 }^{ -9 } }{ \frac{ { 0.05 }^{ 2 } }{ { 2 }^{ 2 } } }$$

Evaluate

$$0.0000000000000288$$

Solution Steps

Calculate 10 to the power of -9 and get \frac{1}{1000000000}.

$$\frac{9\times \frac{1}{1000000000}\left(8\times 10^{-9}-6\times 10^{-9}\right)}{\frac{0.05^{2}}{2^{2}}}$$

Multiply 9 and \frac{1}{1000000000} to get \frac{9}{1000000000}.

$$\frac{\frac{9}{1000000000}\left(8\times 10^{-9}-6\times 10^{-9}\right)}{\frac{0.05^{2}}{2^{2}}}$$

Calculate 10 to the power of -9 and get \frac{1}{1000000000}.

$$\frac{\frac{9}{1000000000}\left(8\times \frac{1}{1000000000}-6\times 10^{-9}\right)}{\frac{0.05^{2}}{2^{2}}}$$

Multiply 8 and \frac{1}{1000000000} to get \frac{1}{125000000}.

$$\frac{\frac{9}{1000000000}\left(\frac{1}{125000000}-6\times 10^{-9}\right)}{\frac{0.05^{2}}{2^{2}}}$$

Calculate 10 to the power of -9 and get \frac{1}{1000000000}.

$$\frac{\frac{9}{1000000000}\left(\frac{1}{125000000}-6\times \frac{1}{1000000000}\right)}{\frac{0.05^{2}}{2^{2}}}$$

Multiply 6 and \frac{1}{1000000000} to get \frac{3}{500000000}.

$$\frac{\frac{9}{1000000000}\left(\frac{1}{125000000}-\frac{3}{500000000}\right)}{\frac{0.05^{2}}{2^{2}}}$$

Subtract \frac{3}{500000000} from \frac{1}{125000000} to get \frac{1}{500000000}.

$$\frac{\frac{9}{1000000000}\times \frac{1}{500000000}}{\frac{0.05^{2}}{2^{2}}}$$

Multiply \frac{9}{1000000000} and \frac{1}{500000000} to get \frac{9}{500000000000000000}.

$$\frac{\frac{9}{500000000000000000}}{\frac{0.05^{2}}{2^{2}}}$$

Calculate 0.05 to the power of 2 and get 0.0025.

$$\frac{\frac{9}{500000000000000000}}{\frac{0.0025}{2^{2}}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{\frac{9}{500000000000000000}}{\frac{0.0025}{4}}$$

Expand \frac{0.0025}{4} by multiplying both numerator and the denominator by 10000.

$$\frac{\frac{9}{500000000000000000}}{\frac{25}{40000}}$$

Reduce the fraction \frac{25}{40000} to lowest terms by extracting and canceling out 25.

$$\frac{\frac{9}{500000000000000000}}{\frac{1}{1600}}$$

Divide \frac{9}{500000000000000000} by \frac{1}{1600} by multiplying \frac{9}{500000000000000000} by the reciprocal of \frac{1}{1600}.

$$\frac{9}{500000000000000000}\times 1600$$

Multiply \frac{9}{500000000000000000} and 1600 to get \frac{9}{312500000000000}.

$$\frac{9}{312500000000000}$$

Factor

$$\frac{3 ^ {2}}{2 ^ {11} \cdot 5 ^ {16}} = 2.88 \times 10^{-14}$$