Solve frac{(9*10^{9})*(4.5*10^-6)*(5*10^-6)}{(15*10^-2)^2}

$$\frac { ( 9 \times 10 ^ { 9 } ) \times ( 4.5 \times 10 ^ { - 6 } ) \times ( 5 \times 10 ^ { - 6 } ) } { ( 15 \times 10 ^ { - 2 } ) ^ { 2 } }$$

Evaluate

$$9$$

Solution Steps

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

$$\frac{9\times 10^{3}\times 4.5\times 5\times 10^{-6}}{\left(15\times 10^{-2}\right)^{2}}$$

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

$$\frac{9\times 10^{-3}\times 4.5\times 5}{\left(15\times 10^{-2}\right)^{2}}$$

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

$$\frac{9\times \frac{1}{1000}\times 4.5\times 5}{\left(15\times 10^{-2}\right)^{2}}$$

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

$$\frac{\frac{9}{1000}\times 4.5\times 5}{\left(15\times 10^{-2}\right)^{2}}$$

Multiply \frac{9}{1000} and 4.5 to get \frac{81}{2000}.

$$\frac{\frac{81}{2000}\times 5}{\left(15\times 10^{-2}\right)^{2}}$$

Multiply \frac{81}{2000} and 5 to get \frac{81}{400}.

$$\frac{\frac{81}{400}}{\left(15\times 10^{-2}\right)^{2}}$$

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

$$\frac{\frac{81}{400}}{\left(15\times \frac{1}{100}\right)^{2}}$$

Multiply 15 and \frac{1}{100} to get \frac{3}{20}.

$$\frac{\frac{81}{400}}{\left(\frac{3}{20}\right)^{2}}$$

Calculate \frac{3}{20} to the power of 2 and get \frac{9}{400}.

$$\frac{\frac{81}{400}}{\frac{9}{400}}$$

Divide \frac{81}{400} by \frac{9}{400} by multiplying \frac{81}{400} by the reciprocal of \frac{9}{400}.

$$\frac{81}{400}\times \frac{400}{9}$$

Multiply \frac{81}{400} and \frac{400}{9} to get 9.

$$9$$

Factor

$$3^{2}$$