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

3 answers

To simplify the expression \( 125^{2/3} \), we can rewrite 125 as a base raised to a power.

First, note that: \[ 125 = 5^3 \]

Now, we can rewrite \( 125^{2/3} \) as: \[ (5^3)^{2/3} \]

Applying the power of a power property, which states \((a^m)^n = a^{m \cdot n}\), we get: \[ 5^{3 \cdot \frac{2}{3}} = 5^{2} \]

Now, to express \( 5^2 \) as a product of identical factors, we have: \[ 5^2 = 5 \times 5 \]

Thus, the simplified form of \( 125^{2/3} \) is: \[ 5 \times 5 \]

In conclusion, the expression \( 125^{2/3} \) simplifies to: \[ 5 \times 5 \]

so 25

Yes, exactly!

The expression \( 125^{2/3} \) simplifies to \( 5 \times 5 \), which is equal to \( 25 \).

Therefore, the simplified form is: \[ 25 \]