Question

Help with simplest product of radicals.

Answer 1

\[\large \sqrt[3]{4x^2} \times \sqrt[3]{8x^7}\]

Answer 2

applying some index rules you have

\[2^{\frac{2}{3}} \times x^{\frac{2}{3}} \times 2 \times x^{\frac{7}{3}}\]

now when multiplying add the powers

\[2^{1 + \frac{2}{3}} \times x^{\frac{2}{3}+\frac{7}{3}}\]

which is simplifies to

\[2x^3 \times 2^{\frac{2}{3}}\]

or

\[2x^3 \sqrt[3]{4}\]