Final answer:
The problem involves simplifying an algebraic expression with exponents and then evaluating the result by substituting given numerical values, following the laws of exponents and understanding negative exponents.
Step-by-step explanation:
The question involves simplifying algebraic expressions using the properties of exponents and then further simplifying the result using a substitution of particular values for given variables. The main goal is to simplify the expression step-by-step to its most reduced form.
When given an expression with exponents like (a-⁶b⁴/2a-⁹b-²)-² · (ab-³), it is essential to apply the laws of exponents which include multiplying powers with the same base by adding exponents, dividing powers with the same base by subtracting exponents, and raising a power to a power by multiplying exponents. Additionally, when an expression has a negative exponent, it signifies that the base needs to be reciprocated, and then the exponent is taken as positive.
To evaluate the expression correctly, after simplification, one would have to substitute any designated numerical values into the simplified algebraic expression. However, it should be noted that the expression might be simplified first before substituting any numerical values.