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

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

Evaluate

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

Solution Steps

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Express \frac{\frac{27}{12500000000000000000000}}{\frac{9}{1000000000000000000}w} as a single fraction.

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

Multiply 12500000000000000000000 and \frac{9}{1000000000000000000} to get 112500.

$$\frac{27}{112500w}$$

Expand

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

Solution Steps

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Express \frac{\frac{27}{12500000000000000000000}}{\frac{9}{1000000000000000000}w} as a single fraction.

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

Multiply 12500000000000000000000 and \frac{9}{1000000000000000000} to get 112500.

$$\frac{27}{112500w}$$