Final answer:
The value of the expression (7m⁻²m²n)² when m=-6 and n=2 is 196, after simplifying inside the parentheses and substituting the given values.
Step-by-step explanation:
When evaluating the expression (7m⁻²m²n)² with given values for m and n, we need to replace m with -6 and n with 2. Upon simplifying the given expression:
- First, we simplify the inside of the parentheses by noting that m⁻²m² = 1 since any number raised to a negative exponent is the reciprocal of that number raised to the corresponding positive exponent, and when we multiply reciprocals, we get 1.
- Next, we substitute the values m = -6 and n = 2 into the expression to get (7·1·2)² which simplifies to (14)².
- Last, squaring 14 gives us 196.
Therefore, the value of the expression when m = -6 and n = 2 is 196.