Final answer:
To simplify (12)/(12^(1/5)), we can rewrite it as (2^2 * 3)^(1/5) and apply the properties of exponents to simplify further.
Step-by-step explanation:
To simplify the expression (12)/(12^(1/5)), we can use the property of rational exponents which states that a^(m/n) is equal to the n-th root of a raised to the m-th power. In this case, we have 12^(1/5), which represents the fifth root of 12. Simplifying further, we can rewrite it as (12)^(1/5) = (2^2 * 3)^(1/5). Using the property of exponents, we can distribute the exponent to each factor inside the parentheses as ((2^2)^(1/5)) * 3^(1/5). Applying the property of exponents again, we get (2^(2/5)) * 3^(1/5). Finally, we can calculate the fifth root of 2^2 which results in 2^(2/5) = 2^(4/10) = 2^(2/5).