9•10^9•|3•10^-9||•6•10^-9|/1•10'10^-2

Let's solve the expression step by step.

The expression is:

\[ \frac{9 \cdot 10^9 \cdot |3 \cdot 10^{-9}| \cdot |6 \cdot 10^{-9}|}{1 \cdot 10^{10^{-2}}} \]

First, we simplify the absolute values. Since both \(3 \cdot 10^{-9}\) and \(6 \cdot 10^{-9}\) are positive, we can drop the absolute value signs:

\[ = \frac{9 \cdot 10^9 \cdot (3 \cdot 10^{-9}) \cdot (6 \cdot 10^{-9})}{1 \cdot 10^{-2}} \]

Now we can simplify the product in the numerator:

\[ = 9 \cdot 3 \cdot 6 \cdot 10^9 \cdot 10^{-9} \cdot 10^{-9} \]

Calculating \(9 \cdot 3 \cdot 6\):

\[ = 9 \cdot 3 = 27 \] \[ = 27 \cdot 6 = 162 \]

Next, we calculate the powers of \(10\):

\[ 10^9 \cdot 10^{-9} \cdot 10^{-9} = 10^{9 - 9 - 9} \] \[ = 10^{-9} \]

Putting it all together in the numerator:

\[ = 162 \cdot 10^{-9} \]

Now, we substitute back into the fraction:

\[ \frac{162 \cdot 10^{-9}}{1 \cdot 10^{-2}} = \frac{162 \cdot 10^{-9}}{10^{-2}} \]

To divide the powers of \(10\), we subtract the exponents:

\[ = 162 \cdot 10^{-9 - (-2)} = 162 \cdot 10^{-9 + 2} = 162 \cdot 10^{-7} \]

Thus, the simplified result is:

\[ 162 \cdot 10^{-7} \]

Or expressed in standard scientific notation:

\[ = 1.62 \cdot 10^{-5} \]

Therefore, the final answer is:

\[ 1.62 \cdot 10^{-5} \]