j) \( 9 \div[6 \div(-2)]= \) k) \( \left[(-2)^{5}-(-3)^{3}\right]^{2}= \) 1) \( (5+3 * 2 \div 6-4) *(4 \div 2-3+6) \div(7-8 \div 2-2)^{2} \) m) \( \left[(17=15)^{3}+(7-12)^{2} \div(6-7) *\left(12-2^{3}\right)\right] \)

Let's unravel the mystery of these mathematical expressions in a way that makes it easier to digest! First up, simplifying the expression \( 9 \div[6 \div(-2)] \) is all about following the order of operations, a.k.a. PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). When we resolve \( 6 \div(-2) \), we get -3. Then, \( 9 \div(-3) \) equals -3! Now, diving into \( \left[(-2)^{5}-(-3)^{3}\right]^{2} \) involves crunching those exponents first! \( (-2)^{5} \) gives us -32 and \( (-3)^{3} \) gives -27. Thus, we have \(-32 - (-27) = -32 + 27 = -5\), and squaring it, we get \(25\). For the expression \( (5 + 3 * 2 \div 6 - 4) * (4 \div 2 - 3 + 6) \div (7 - 8 \div 2 - 2)^{2} \), let’s break it down nicely: The left part evaluates to 3 for the first half and 1 for the second half. The denominator simplifies to 1, leading us to conclude that the whole expression equals 3. Consider the statement \( \left[(17=15)^{3}+(7-12)^{2} \div(6-7) *\left(12-2^{3}\right)\right] \). It’s worthy of a laugh, as \( (17=15)^{3} \) is false and contributes 0; however, focusing on the \( (7-12)^{2} \) gives 25, and \( (12-2^{3}) = 4 \). It's a delightful web of math! So, happy calculating! The world of math is a playground waiting for your exploration.