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

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:

Option C

3: 2

step-by-step explanation:

shorter piece is 2: 3, so just reverse it, and you get 3: 2

since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

  (x^4) ^ ¼   = 81 ^ ¼  

  81 = 3^4     so (3 ^ 4) ^ ¼   =   3 ^ 1   = 3

by hand: (3 ^ 4) ^ ¼   =   3 ^ (4 x ¼) = 3 ^ 1   = 3   (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation: