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# 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}= ∛9^{2}

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.

## 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.

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