Respuesta :

Louli
I added a screenshot of the complete question.

Answer:
True

Explanation:
Rules of the root are as follows:
[tex] \sqrt[n]{x} = x^{ \frac{1}{n}} \\ \sqrt[n]{x} * \sqrt[n]{y} = \sqrt[n]{xy} \\ \sqrt[n]{ \frac{x}{y}} = \frac{ \sqrt[n]{x} }{ \sqrt[n]{y} } [/tex]

Now the given is:
[tex] \sqrt[n]{a} = a^{ \frac{1}{n}} [/tex]
This rule is the same as the first rule mentioned above, therefore, it is correct.
We use this rule to convert roots into powers which facilitates solving the problems given

Hope this helps :0

Ver imagen Louli
facundo3141592

Here we want to see if for a, a non-negative real number, and n, a positive integer, is true or false that:

[tex]a^{1/n} = \sqrt[n]{a}[/tex]

We will see that it is true.

So let's try to prove that, we already know that:

[tex]\sqrt{x^2} = x[/tex]

Remember that.

Now, let's start with:

[tex]a^{1/n}[/tex]

If we elevate this to the n-th power, we get:

[tex](a^{1/n})^n = a^{n/n} = a^1 = a[/tex]

Similarly, at the right side we have:

[tex]\sqrt[n]{a}^n = a[/tex]

Notice that in both cases when we elevated to the n-th power, we got the same thing, then these are equivalent, then:

[tex](a^{1/n})^n = (\sqrt[n]{a})^n\\\\a^{1/n} = \sqrt[n]{a}[/tex]

Is true.

If you want to learn more, you can read:

https://brainly.com/question/219134