Final answer:
The expression 3y⁸/12y³ simplifies to ¼y⁵ by dividing the coefficients and subtracting the exponents of the variable 'y'.
Step-by-step explanation:
To simplify the expression 3y⁸/12y³, we need to first divide the coefficients and then use the rules for dividing exponential terms. We start by dividing 3 by 12, which simplifies to 1/4 since 3 is a factor of 12. Then we apply the rule for division of exponentials, which states to subtract the exponent of the denominator from the exponent of the numerator. The exponents on our variable 'y' are 8 (for y⁸) and 3 (for y³), so we subtract 3 from 8, leaving us with y raised to the power of 5 (y⁵).
Therefore, the simplified form of the expression is: ¼y⁵.
When performing operations on exponential terms, we should always express our final answer with positive exponents. This problem demonstrates the rule of subtracting exponents when dividing with the same base and reinforces the concept that the simplified expression should have positive exponents only.