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

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

Evaluate

$$\frac{81}{1000000000}=0.000000081$$

Solution Steps

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

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

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

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

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

$$\frac{9\times \frac{1}{1000}\times 6\times 6}{\left(2\times 10^{3}\right)^{2}}$$

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

$$\frac{\frac{9}{1000}\times 6\times 6}{\left(2\times 10^{3}\right)^{2}}$$

Multiply \frac{9}{1000} and 6 to get \frac{27}{500}.

$$\frac{\frac{27}{500}\times 6}{\left(2\times 10^{3}\right)^{2}}$$

Multiply \frac{27}{500} and 6 to get \frac{81}{250}.

$$\frac{\frac{81}{250}}{\left(2\times 10^{3}\right)^{2}}$$

Calculate 10 to the power of 3 and get 1000.

$$\frac{\frac{81}{250}}{\left(2\times 1000\right)^{2}}$$

Multiply 2 and 1000 to get 2000.

$$\frac{\frac{81}{250}}{2000^{2}}$$

Calculate 2000 to the power of 2 and get 4000000.

$$\frac{\frac{81}{250}}{4000000}$$

Express \frac{\frac{81}{250}}{4000000} as a single fraction.

$$\frac{81}{250\times 4000000}$$

Multiply 250 and 4000000 to get 1000000000.

$$\frac{81}{1000000000}$$

Factor

$$\frac{3 ^ {4}}{2 ^ {9} \cdot 5 ^ {9}} = 8.1 \times 10^{-8}$$