Solve 5*10^-9*(-2)*10^-9/left(3*10^-2right)^2

$$\frac{ 5 \times { 10 }^{ -9 } \times (-2) \times { 10 }^{ -9 } }{ { \left(3 \times { 10 }^{ -2 } \right) }^{ 2 } }$$

Evaluate

$$-\frac{1}{90000000000000}\approx -1.111111111 \cdot 10^{-14}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -9 and -9 to get -18.

$$\frac{5\times 10^{-18}\left(-2\right)}{\left(3\times 10^{-2}\right)^{2}}$$

Calculate 10 to the power of -18 and get \frac{1}{1000000000000000000}.

$$\frac{5\times \frac{1}{1000000000000000000}\left(-2\right)}{\left(3\times 10^{-2}\right)^{2}}$$

Multiply 5 and \frac{1}{1000000000000000000} to get \frac{1}{200000000000000000}.

$$\frac{\frac{1}{200000000000000000}\left(-2\right)}{\left(3\times 10^{-2}\right)^{2}}$$

Multiply \frac{1}{200000000000000000} and -2 to get -\frac{1}{100000000000000000}.

$$\frac{-\frac{1}{100000000000000000}}{\left(3\times 10^{-2}\right)^{2}}$$

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

$$\frac{-\frac{1}{100000000000000000}}{\left(3\times \frac{1}{100}\right)^{2}}$$

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

$$\frac{-\frac{1}{100000000000000000}}{\left(\frac{3}{100}\right)^{2}}$$

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

$$\frac{-\frac{1}{100000000000000000}}{\frac{9}{10000}}$$

Divide -\frac{1}{100000000000000000} by \frac{9}{10000} by multiplying -\frac{1}{100000000000000000} by the reciprocal of \frac{9}{10000}.

$$-\frac{1}{100000000000000000}\times \frac{10000}{9}$$

Multiply -\frac{1}{100000000000000000} and \frac{10000}{9} to get -\frac{1}{90000000000000}.

$$-\frac{1}{90000000000000}$$

Factor

$$-\frac{1}{90000000000000} = -1.111111111111111 \times 10^{-14}$$