Evaluate 125^(4/3)

Problem

125^(4/3)

Solution

1. Rewrite the expression using the property of rational exponents a^(m/n)=(√(n,a))^m

125^(4/3)=(√(3,125))^4

2. Evaluate the cube root of the base by identifying that 5^3=125

√(3,125)=5

3. Substitute the result back into the expression.

5^4

4. Calculate the final value by multiplying 5 by itself four times.

5×5×5×5=625

Final Answer

125^(4/3)=625

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