## What is the following product? Assume x ≥ 0 \sqrt[3]{x^{2} } . \sqrt[4]{x^{3} } A. x\sqrt{x} B.

Question

What is the following product? Assume x ≥ 0

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

A. x\sqrt{x}

B. \sqrt[12]{x^{5} }

C. x(\sqrt[12]{x^{5} } )

D. x6

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1 week 2021-10-10T20:50:19+00:00 1 Answer 0

1. For this case we must multiply the following expression:

By definition of properties of otencias and roots we have:

We rewrite the terms of the expression:

So, we have:

Applying the above definition we have:

We multiply the exponents:

We combine using the product rule for radicals.

By definition of multiplication properties of powers of the same base, we put the same base and add the exponents: