Solve left(3*10^-2right)^2divleft(6*10^-1right)^2

$${ \left(3 \times { 10 }^{ -2 } \right) }^{ 2 } \div { \left(6 \times { 10 }^{ -1 } \right) }^{ 2 }$$

Evaluate

$$\frac{1}{400}=0.0025$$

Solution Steps

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

$$\frac{\left(3\times \frac{1}{100}\right)^{2}}{\left(6\times 10^{-1}\right)^{2}}$$

Multiply 3 and \frac{1}{100} to get \frac{3}{100}.

$$\frac{\left(\frac{3}{100}\right)^{2}}{\left(6\times 10^{-1}\right)^{2}}$$

Calculate \frac{3}{100} to the power of 2 and get \frac{9}{10000}.

$$\frac{\frac{9}{10000}}{\left(6\times 10^{-1}\right)^{2}}$$

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

$$\frac{\frac{9}{10000}}{\left(6\times \frac{1}{10}\right)^{2}}$$

Multiply 6 and \frac{1}{10} to get \frac{3}{5}.

$$\frac{\frac{9}{10000}}{\left(\frac{3}{5}\right)^{2}}$$

Calculate \frac{3}{5} to the power of 2 and get \frac{9}{25}.

$$\frac{\frac{9}{10000}}{\frac{9}{25}}$$

Divide \frac{9}{10000} by \frac{9}{25} by multiplying \frac{9}{10000} by the reciprocal of \frac{9}{25}.

$$\frac{9}{10000}\times \frac{25}{9}$$

Multiply \frac{9}{10000} and \frac{25}{9} to get \frac{1}{400}.

$$\frac{1}{400}$$

Factor

$$\frac{1}{2 ^ {4} \cdot 5 ^ {2}} = 0.0025$$