To find the product of [tex]\((-2 \sqrt{20k})(5 \sqrt{8k^3})\)[/tex], we need to follow these steps:
1. Multiply the coefficients: First, multiply the numerical coefficients outside of the square roots.
[tex]\[
(-2) \cdot 5 = -10
\][/tex]
So the combined coefficient is [tex]\(-10\)[/tex].
2. Multiply the terms under the radicals:
[tex]\[
\sqrt{20k} \cdot \sqrt{8k^3}
\][/tex]
Using the property of radicals [tex]\(\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}\)[/tex],
[tex]\[
\sqrt{20k \cdot 8k^3} = \sqrt{160k \cdot k^3} = \sqrt{160k^4}
\][/tex]
3. Combine the results:
[tex]\[-10\sqrt{160k^4}\][/tex]
Thus, the expression equivalent to the given product is:
[tex]\[
-10 \sqrt{160 k^4}
\][/tex]
Therefore, the correct choice is:
[tex]\[
-10 \sqrt{160 k^4}
\][/tex]
