Question

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

4a9
9a4
fourth root of a to the ninth power
ninth root of a to the fourth power

Answer 1

Explanation:

`\sqrt[n]{a^m}=a^(m)/(n)\\\\\large\huge\boxed{a^(4)/(9)=\sqrt[9]{a^4}}`

Answer 2

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

Ninth root of a to the fourth power.

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^{(4)/(9)}`

Now, we know that:

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

Here we have:

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

Hence, the expression cold be written as:

`a^{(4)/(9)}=\sqrt[9]{a^4}`