Sure, let's break down the given expression step-by-step to find its equivalent form.
The expression provided is:
[tex]\[
\left(2 \cdot 10^6\right) \div \left(3 \cdot 10^{-2}\right) \cdot \left(3 \cdot 10^2\right)
\][/tex]
First, let's start with the division part:
[tex]\[
\left(2 \cdot 10^6\right) \div \left(3 \cdot 10^{-2}\right)
\][/tex]
We can simplify this as follows:
[tex]\[
\frac{2 \cdot 10^6}{3 \cdot 10^{-2}}
\][/tex]
When dividing numbers in scientific notation, we can divide the coefficients and subtract the exponents in the denominator from the numerator. So,
[tex]\[
\frac{2}{3} \cdot 10^{6 - (-2)} = \frac{2}{3} \cdot 10^{6 + 2} = \frac{2}{3} \cdot 10^8
\][/tex]
Next, let's handle the multiplication part of the original expression:
[tex]\[
\left(\frac{2}{3} \cdot 10^8 \right) \cdot \left(3 \cdot 10^2\right)
\][/tex]
Again, multiply the coefficients and add the exponents:
[tex]\[
\left(\frac{2}{3} \cdot 3\right) \cdot 10^{8 + 2} = 2 \cdot 10^{10}
\][/tex]
Thus, the simplified form of the given expression is:
[tex]\[
2 \cdot 10^{10}
\][/tex]
Finally, looking at the options provided:
(A) [tex]\(2 \cdot 10^{-4}\)[/tex]
(B) [tex]\(2 \cdot 10^4\)[/tex]
(C) [tex]\(1.8 \cdot 10^6\)[/tex]
(D) [tex]\(2 \cdot 10^{10}\)[/tex]
The correct answer is:
[tex]\[
\boxed{D}
\][/tex]
