Question

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

Answer 1

Given expression in exponential form : $a^{\frac{4}{9} }$.

We need to convert it into radical form.

Please note: When we convert an exponential to radical form, the top number goes in the exponent of the term and bottom number of the fraction goes in the radical sign to make it nth radical.

We can apply following rule:

$(a)^{\frac{m}{n}}= \sqrt[n]{x^m}$.

Therefore,

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

Therefore, correct option is : D. ninth root of a to the fourth power.