Rewrite the expression as a product of identical factors to simplify 125^2/3

. Submit your answer in simplified form. (1 point)

1 answer

To simplify the expression \( 125^{2/3} \), we can first rewrite \( 125 \) as a power of \( 5 \):

\[ 125 = 5^3 \]

Now substituting this into our expression:

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

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

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

Now, \( 5^2 \) can be expressed as a product of identical factors:

\[ 5^2 = 5 \cdot 5 \]

Therefore, the simplified form of \( 125^{2/3} \) is:

\[ \boxed{5 \cdot 5} \]