How to Simplify 125^(2/3) for a 13-Year-Old Student

Step-by-step explanation for simplifying the expression 125 raised to the power of 2/3, designed for a 13-year-old student.

Let's simplify 125^(2/3) step by step.

  1. 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.
  2. Rewrite the expression: 125^(2/3) = (125^(1/3))^2. This means first find the cube root of 125, then square the result.
  3. 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.
  4. Square the result: Now, square 5: 5² = 25.
  5. Final answer: So, 125^(2/3) = 25.

Summary: 125^(2/3) = (cube root of 125) squared = 5² = 25.

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