Final answer:
The simplified expression without negative exponents is (1/4)(a^5/b^2), achieved by flipping bases with negative exponents to the opposite part of the fraction and then simplifying.
Step-by-step explanation:
The student is inquiring about how to simplify an algebraic expression with negative exponents. The expression provided is 4a2b-2 / 16a-3b. Simplifying this expression involves two main steps: first, we eliminate negative exponents by using the rule that a negative exponent in the numerator or denominator flips the base to the opposite part of the fraction (numerator to denominator or vice versa). Second, we simplify the expression by dividing coefficients and subtracting exponents of like bases.
Let's apply these steps to the given expression. Since a-3 is in the denominator, it becomes a3 in the numerator, and similarly, b-2 flips to the denominator, becoming b2. Therefore, eliminating negative exponents, we have:
(4a2+3)/(16b2)
Now we simplify further by dividing the coefficients and subtracting the exponents:
(4/16)(a5/b2) = (1/4)(a5/b2)
The simplified expression with all negative exponents eliminated is (1/4)(a5/b2).