Final answer:
The original expression can be re-written based on the rules of exponents and then simplified step by step, ending up with a final answer of 16a^4/b^4.
Step-by-step explanation:
The given expression is ((a^(-1)b)/(2))^(-4). To simplify the expression, remember that when you raise a power to a power, you multiply the exponents. Then, recall that a negative exponent indicates a reciprocal, so a^(-1) equals 1/a, (or a to the power of negative 1 is equal to 1 divided by a). Here’s how we simplify:
Step 1
: Substitute 1/a for a^(-1) in the expression, and you get ((1/a)*b/2)^(-4).
Step 2
: Next, understand that raising to the power of -4 means taking the reciprocal and raising to the power of 4, so you obtain (2/(b/a))^4.
Step 3
: Simplify b/a to arrive at 2a/b. Thus, you are left with (2a/b)^4.
Step 4
: Expand this to get the final answer; (2a/b)^4 expands to 16a^4/b^4.
Learn more about Simplifying Expressions