simplify (-2\\sqrt{20k})(5\\sqrt{8k^{3}}) completely.\n-10k^{4}\\sqrt{16}\n-10k^{2}\\sqrt{16}\n-40k^{4}\\sqrt…

Explanation:

Step1: Simplify square - root terms

Simplify $\sqrt{20k}=\sqrt{4\times5k}=2\sqrt{5k}$ and $\sqrt{8k^{3}}=\sqrt{4k^{2}\times2k}=2k\sqrt{2k}$.

Step2: Multiply the coefficients and the square - root parts

The original expression $(-2\sqrt{20k})(5\sqrt{8k^{3}})$ becomes $(-2\times5)\times(\sqrt{20k}\times\sqrt{8k^{3}})$. The product of the coefficients is $- 10$. And $\sqrt{20k}\times\sqrt{8k^{3}}=\sqrt{20k\times8k^{3}}=\sqrt{160k^{4}}$.

Step3: Simplify the square - root result

$\sqrt{160k^{4}}=\sqrt{16\times10\times k^{4}} = 4k^{2}\sqrt{10}$.

Step4: Combine the results

$-10\times4k^{2}\sqrt{10}=-40k^{2}\sqrt{10}$.

Answer:

$-40k^{2}\sqrt{10}$