Solve frac{(9*10^{9})*(2,0*10^-6)*(5,0*10^-6)}{(3,0*10^-2)^2}

$$\frac { ( 9 \cdot 10 ^ { 9 } ) \cdot ( 2,0 \cdot 10 ^ { - 6 } ) \cdot ( 5,0 \cdot 10 ^ { - 6 } ) } { ( 3,0 \times 10 ^ { - 2 } ) ^ { 2 } }$$

Evaluate

$$100$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 9 and -6 to get 3.

$$\frac{9\times 10^{3}\times 2\times 5\times 10^{-6}}{\left(3\times 10^{-2}\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 3 and -6 to get -3.

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

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$\frac{9\times \frac{1}{1000}\times 2\times 5}{\left(3\times 10^{-2}\right)^{2}}$$

Multiply 9 and \frac{1}{1000} to get \frac{9}{1000}.

$$\frac{\frac{9}{1000}\times 2\times 5}{\left(3\times 10^{-2}\right)^{2}}$$

Multiply \frac{9}{1000} and 2 to get \frac{9}{500}.

$$\frac{\frac{9}{500}\times 5}{\left(3\times 10^{-2}\right)^{2}}$$

Multiply \frac{9}{500} and 5 to get \frac{9}{100}.

$$\frac{\frac{9}{100}}{\left(3\times 10^{-2}\right)^{2}}$$

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

$$\frac{\frac{9}{100}}{\left(3\times \frac{1}{100}\right)^{2}}$$

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

$$\frac{\frac{9}{100}}{\left(\frac{3}{100}\right)^{2}}$$

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

$$\frac{\frac{9}{100}}{\frac{9}{10000}}$$

Divide \frac{9}{100} by \frac{9}{10000} by multiplying \frac{9}{100} by the reciprocal of \frac{9}{10000}.

$$\frac{9}{100}\times \frac{10000}{9}$$

Multiply \frac{9}{100} and \frac{10000}{9} to get 100.

$$100$$

Factor

$$2^{2}\times 5^{2}$$