Question

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

Answer 1

thats wrong

Answer 2

To simplify \( 125^{2/3} \), we can start by expressing 125 as a power of 5:

\[
125 = 5^3
\]

Now we substitute this into the expression:

\[
125^{2/3} = (5^3)^{2/3}
\]

Using the property of exponents \((a^m)^n = a^{m \cdot n}\), we can simplify this further:

\[
(5^3)^{2/3} = 5^{3 \cdot (2/3)} = 5^2
\]

Now, we have:

\[
5^2 = 25
\]

Thus, we can express \( 125^{2/3} \) as a product of identical factors:

\[
25 = 5 \cdot 5
\]

So the final answer in simplified form is:

\[
\boxed{25}
\]

Answer 3

I apologize for any confusion in my previous response. Let’s carefully go through the steps to simplify \( 125^{2/3} \) correctly.

Starting with \( 125^{2/3} \):

1. **Express 125 as a power of 5**:
\[
125 = 5^3
\]

2. **Substitute into the expression**:
\[
125^{2/3} = (5^3)^{2/3}
\]

3. **Use the exponent rule \((a^m)^n = a^{m \cdot n}\)**:
\[
(5^3)^{2/3} = 5^{3 \cdot (2/3)} = 5^{2}
\]

4. **Calculate \(5^2\)**:
\[
5^2 = 25
\]

The expression \( 125^{2/3} \) simplifies to 25, which can be expressed as a product of identical factors:

\[
25 = 5 \times 5
\]

Thus, the simplified form expressed as a product of identical factors is:

\[
\boxed{5 \times 5}
\]

If you meant something different by "identical factors," please clarify. Thank you!