Final answer:
To completely simplify the expression 48a²¹ b⁵ / 16a²¹ b⁴, we divide the coefficients and subtract the exponents of like bases, resulting in a final simplified expression of 3b.
Step-by-step explanation:
To simplify the expression 48a²¹ b⁵ / 16a²¹ b⁴ completely, you'll want to reduce both the numerical and variable parts of the fraction. The numbers 48 and 16 can be divided by 16, giving us 3 in the numerator and 1 in the denominator. Now, looking at the variables, since the base and exponent are the same for a in both the numerator and denominator, they cancel out. For the variable b, b⁵ in the numerator and b⁴ in the denominator leaves us with just b in the numerator because we subtract the exponents (5 - 4 = 1). As a result, our final simplified expression is 3b.