When 9^2/3 is written in the simplest radical form, which value remains under the radical?

Solution:

Given, the value is 9^2/3

We find that 9 is raised to the power 2/3, which is a rational exponent.

We need to find the value that remains under the radical when 9^2/3 is written in the simplest radical form.

Using exponent property for radicals,

a^m/n = \(\sqrt[n]{x^{m}}\)

Given value can be written as

9^2/3= ∛9²

9^2/3= ∛81

On further simplification,

9^2/3= ∛(3×3×3×3)

9^2/3= ∛(3³×3)

Now pulling out 3 from radical, we get

9^2/3= 3∛3

Therefore, the simplest form of expression will be 3∛3, and 3 will remain under radical.

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When 9^2/3 is written in the simplest radical form, which value remains under the radical?

Summary:

The expression 9^2/3 written in the simplest radical form is 3∛3 and the value 3 remains under the radical.