Rewrite the expression as a product of identical factors to simplify 125^ 2/3. Submit your answer in simplified form.
To simplify, we can rewrite 125 as 5^3. Then, we can apply the exponent rule (a^m)^n = a^(m*n) to 5^3 raised to the power of 2/3.
(5^3)^(2/3) = 5^(3*(2/3))
= 5^(6/3)
= 5^2
Therefore, the expression 125^(2/3) can be simplified to 5^2.
To rewrite the expression 125^2/3 as a product of identical factors, we can use the fact that a fractional exponent represents a root.
Since 2/3 is a cube root, we can rewrite the expression as a cube root of 125 raised to the power of 2:
125^2/3 = (125^(1/3))^2
The cube root of 125 is 5 because 5 * 5 * 5 = 125.
Therefore, the expression can be simplified as:
125^2/3 = (5^3)^2 = 5^(3 * 2) = 5^6
So, the simplified form of 125^2/3 is 5^6.