(6,67x2000x2000:(6,67x10^-9))^0,5

To solve the expression \((6.67 \times 2000 \times 2000 : (6.67 \times 10^{-9}))^{0.5}\), we will first rewrite it in a clearer form and then compute it step-by-step.

1. Rewrite the expression: The colon ":" denotes division, so we have:

   \[ (6.67 \times 2000 \times 2000 / (6.67 \times 10^{-9}))^{0.5} \]

2. Simplify the expression: We can cancel out the \(6.67\) in the numerator and denominator.

   \[ (2000 \times 2000 / (10^{-9}))^{0.5} \]

3. Calculate \(2000 \times 2000\):

   \[ 2000 \times 2000 = 4,000,000 \]

4. Divide by \(10^{-9}\):

   \[ 4,000,000 / (10^{-9}) = 4,000,000 \times 10^{9} = 4 \times 10^{15} \]

5. Take the square root:

   \[ (4 \times 10^{15})^{0.5} = 2 \times 10^{7.5} \]

   Breaking \(10^{7.5}\) down further gives us:

   \[ 10^{7.5} = 10^{7} \times 10^{0.5} = 10^{7} \times \sqrt{10} \]

6. Final Result:

   Therefore, the final expression is:

   \[ 2 \times 10^{7} \times \sqrt{10} \]

7. Approximate calculation:

   Since \(\sqrt{10} \approx 3.162\), we can estimate:

   \[ 2 \times 10^{7} \times 3.162 \approx 6.324 \times 10^{7} \]

So, the result for the expression \((6.67 \times 2000 \times 2000 : (6.67 \times 10^{-9}))^{0.5}\) is approximately:

\[ 6.324 \times 10^{7} \]