Question

8. Given x>0, rewrite the following expression in simplest radical form.

Answer 1

Given:

There are given the expression:

`√(16x^4)\cdot\sqrt[4]{16x^2}`

Step-by-step explanation:

To find the expression, we need to simplify the radicals:

So,

From the expression:

`√(16x^4)\cdot\sqrt[4]{16x^2}=4x^2\cdot\sqrt[4]{16x^2}`

Now,

`\begin{gathered} 4x^2\sqrt[4]{16x^2}=4x^2\cdot2\sqrt[4]{x^2} \\ =8x^2\sqrt[4]{x^2} \end{gathered}`

Final answer:

Hence, the simplified radical form is shown below:

`8x^2\sqrt[4]{x^2}`