Question

Algebra II engenuity

Answer 1

Answer: First option.

Explanation:

Knwing that we must find which is the equivalent expression of the expression
`\sqrt[4]{x^(10)}`, it is important to remember the Product of powers property, which states the following:

`(a^m)(a^n)=a^((m+n))`

The we can rewrite the expression:

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

Remember that:

`\sqrt[n]{a^n}=a`

Then we get this equivalent expression:

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

Answer 2

First Option

Explanation:

Given expression is:

`\sqrt[4]{x^(10)}`

The radicand's exponent will be made multiple of 4 to make the calculations easy

So,

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

The 4 outside the radical means that the power that will be multiplied with the exponents will be 1/4

So,

`= x^{(8*(1)/(4))} * x^{(2*(1)/(4))}\\=x^2 \sqrt[4]{x^2}`

As x^2 couldn't be solved using radical, it will remain inside the radical.

So the correct answer is first option..