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

1 answer

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

\[ 125 = 5^3 \]

Now, substituting that into the expression gives us:

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

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

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

Now we calculate \( 5^2 \):

\[ 5^2 = 25 \]

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

\[ \boxed{25} \]

To express \( 25 \) as a product of identical factors, we can write:

\[ 25 = 5 \times 5 \]

So as a product of identical factors, the answer is:

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