91Ó°ÊÓ

First, locate the radicand (the expression under the fourth root) in the radical expression. The radicand is the part of the expression we need to analyze further.

Break down the radicand into its prime factors. This will help us to identify if there are any factors that can be raised to the fourth power.

Examine the prime factors and check if any factors have an exponent that is a multiple of 4 (i.e., 4, 8, 12, etc.). If any factors have such exponents, they can be simplified.

If there are factors raised to the fourth power, then the expression isn't completely simplified. Simplify the expression by taking the fourth root of those factors and rewriting the expression accordingly.

Once you have simplified the expression as much as possible, make sure there are no remaining factors in the radicand with exponents that are multiples of 4. If there are none, the radical expression is fully simplified. For example, let's check if the expression \(\sqrt[4]{1600}\) is completely simplified: 1. Identify the radicand: The radicand is 1600. 2. Factor the radicand: The prime factors of 1600 are \(2^6 \cdot 5^2\). 3. Look for factors raised to the fourth power: There are no factors with an exponent that is a multiple of 4. 4. Rewrite the expression, if necessary: The original expression can be rewritten as \(\sqrt[4]{2^6 \cdot 5^2} \). 5. Ensure there are no remaining factors with fourth-power exponents: As there are no factors with exponents that are multiples of 4, the expression \(\sqrt[4]{2^6 \cdot 5^2}\) is completely simplified.