Question

Rewrite the expression as a product of identical factors to simplify 125^2/3
. Submit your answer in simplified form. (1 point)
Incorrect

Remember to simplify using the denominator of the exponent before applying the numerator on the exponent.

Answer 1

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

1. Start with \( 125^{2/3} \).

2. Recognize that \( 125 \) can be expressed as \( 5^3 \) since \( 5 \times 5 \times 5 = 125 \).

3. Substitute \( 125 \) with \( 5^3 \):
\[
125^{2/3} = (5^3)^{2/3}
\]

4. Apply the power of a power property \((a^m)^n = a^{m \cdot n}\):
\[
(5^3)^{2/3} = 5^{3 \cdot (2/3)} = 5^2
\]

5. Simplify \( 5^2 \):
\[
5^2 = 25
\]

Thus, the simplified form of \( 125^{2/3} \) is **25**.