Let's simplify 125^(2/3) step by step.
- Understand the exponent: The exponent 2/3 means we have to raise 125 to the power of 2, and take the cube root (because of the 3 in the denominator), or vice versa.
- Rewrite the expression: 125^(2/3) = (125^(1/3))^2. This means first find the cube root of 125, then square the result.
- Find the cube root of 125: The cube root means the number that, when multiplied by itself three times, gives 125. Since 5 × 5 × 5 = 125, the cube root of 125 is 5.
- Square the result: Now, square 5: 5² = 25.
- Final answer: So, 125^(2/3) = 25.
Summary: 125^(2/3) = (cube root of 125) squared = 5² = 25.