Evaluate 625^(1/4)

Problem

625(1/4)

Solution

1. Identify the operation as finding the fourth root of the number 625

2. Rewrite the expression using radical notation to visualize the root.

√(4,625)

3. Factor the radicand into its prime factors to find a number that, when multiplied by itself four times, equals 625

625=5×125

625=5×5×25

625=5×5×5×5

4. Apply the property of exponents where (an)(1/n)=a

(5)(1/4)=5

Final Answer

625(1/4)=5

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