Rewrite the expression as a product of identical factors to simplify 125^2/3. Write the answer in simplified form

Answer 1

To simplify the expression \( 125^{2/3} \) and rewrite it as a product of identical factors, we will follow these steps:

1. Identify the base: The base here is \( 125 \).
2. Express \( 125 \) as a power: We can find that \( 125 = 5^3 \).
3. Substitute into the expression: \[ 125^{2/3} = (5^3)^{2/3} \]
4. Apply the power of a power property: This property states that \((a^m)^n = a^{mn}\). Thus, \[ (5^3)^{2/3} = 5^{(3 \cdot \frac{2}{3})} = 5^2 \]
5. Simplify \( 5^2 \): \[ 5^2 = 25 \]

So, the expression \( 125^{2/3} \) simplified is \( 25 \).

Finally, the answer in simplified form is: \[ 25 \]