The **Hierarchy of Mathematical Operations** tells us the correct order to solve a math problem that has different operations like addition, subtraction, multiplication, division, and parentheses. This order makes sure that everyone gets the same answer when solving the same problem. The hierarchy is often remembered with the phrase **PEMDAS**, which stands for: 1. **Parentheses (P)**: Do any calculations inside parentheses first. For example, in $(3 + (2 \times 4))$, calculate $(2 \times 4)$ inside the parentheses before adding the 3. 2. **Exponents (E)**: Next, handle exponents (like squares or cubes). For example, in $(5^2 + 3)$, calculate $(5^2)$ (which is 25) before adding 3. 3. **Multiplication and Division (MD)**: Do any multiplication and division next, working from left to right. For example, in $(8 \div 4 \times 2)$, you start with $(8 \div 4 = 2)$, then multiply by 2 for the answer, 4. 4. **Addition and Subtraction (AS)**: Lastly, do any addition and subtraction, also from left to right. For example, in $(10 - 3 + 2)$, start with $(10 - 3 = 7)$, then add 2 to get 9. So if you see a problem like $(4 + 3 \times (6 - 2)^2 \div 2)$: 1. First, solve inside parentheses: $(6 - 2 = 4)$. 2. Then, handle the exponent: $(4^2 = 16)$. 3. Next, do the multiplication and division from left to right: $(3 \times 16 = 48)$, and then $(48 \div 2 = 24)$. 4. Finally, do the addition: $(4 + 24 = 28)$. The answer would be 28. This order helps avoid mistakes and confusion, ensuring everyone gets the same result.