Question

Which of the following is the radical expression of a to the four ninths power?

Answer 1

Step-by-step explanation:

$\sqrt[n]{a^m}=a^\frac{m}{n}\\\\\large\huge\boxed{a^\frac{4}{9}=\sqrt[9]{a^4}}$

Answer 2

Answer:

The radical expression which represents a to the four ninths power is:

         Ninth root of a to the fourth power.

Step-by-step explanation:

We are asked to find the radical expression for the word phrase:

             a to the four ninths power.

i.e. mathematically it could be written as:

$a^{\dfrac{4}{9}}$

Now, we know that:

$a^{\dfrac{m}{n}}=(a^m)^{\dfrac{1}{n}}=\sqrt[n]{a^m}$

Here we have:

$m=4\ \text{and}\ n=9$

Hence, the expression cold be written as:

$a^{\dfrac{4}{9}}=\sqrt[9]{a^4}$