Solve frac{9*10^{9}*4*10^-16*6*10^-16}{(3*10^-9)^2}

$$\frac { 9 \cdot 10 ^ { 9 } \cdot 4 \cdot 10 ^ { - 16 } \cdot 6 \cdot 10 ^ { - 16 } } { ( 3 \cdot 10 ^ { - 9 } ) ^ { 2 } }$$

Evaluate

$$\frac{3}{12500}=0.00024$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 9 and -16 to get -7.

$$\frac{9\times 10^{-7}\times 4\times 6\times 10^{-16}}{\left(3\times 10^{-9}\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add -7 and -16 to get -23.

$$\frac{9\times 10^{-23}\times 4\times 6}{\left(3\times 10^{-9}\right)^{2}}$$

Calculate 10 to the power of -23 and get \frac{1}{100000000000000000000000}.

$$\frac{9\times \frac{1}{100000000000000000000000}\times 4\times 6}{\left(3\times 10^{-9}\right)^{2}}$$

Multiply 9 and \frac{1}{100000000000000000000000} to get \frac{9}{100000000000000000000000}.

$$\frac{\frac{9}{100000000000000000000000}\times 4\times 6}{\left(3\times 10^{-9}\right)^{2}}$$

Multiply \frac{9}{100000000000000000000000} and 4 to get \frac{9}{25000000000000000000000}.

$$\frac{\frac{9}{25000000000000000000000}\times 6}{\left(3\times 10^{-9}\right)^{2}}$$

Multiply \frac{9}{25000000000000000000000} and 6 to get \frac{27}{12500000000000000000000}.

$$\frac{\frac{27}{12500000000000000000000}}{\left(3\times 10^{-9}\right)^{2}}$$

Calculate 10 to the power of -9 and get \frac{1}{1000000000}.

$$\frac{\frac{27}{12500000000000000000000}}{\left(3\times \frac{1}{1000000000}\right)^{2}}$$

Multiply 3 and \frac{1}{1000000000} to get \frac{3}{1000000000}.

$$\frac{\frac{27}{12500000000000000000000}}{\left(\frac{3}{1000000000}\right)^{2}}$$

Calculate \frac{3}{1000000000} to the power of 2 and get \frac{9}{1000000000000000000}.

$$\frac{\frac{27}{12500000000000000000000}}{\frac{9}{1000000000000000000}}$$

Divide \frac{27}{12500000000000000000000} by \frac{9}{1000000000000000000} by multiplying \frac{27}{12500000000000000000000} by the reciprocal of \frac{9}{1000000000000000000}.

$$\frac{27}{12500000000000000000000}\times \frac{1000000000000000000}{9}$$

Multiply \frac{27}{12500000000000000000000} and \frac{1000000000000000000}{9} to get \frac{3}{12500}.

$$\frac{3}{12500}$$

Factor

$$\frac{3}{2 ^ {2} \cdot 5 ^ {5}} = 0.00024$$