Answer:
-1
Step-by-step explanation:
The PEMDAS rule is an acronym representing the order of operations in math:
- Parentheses
- Exponents
- Multiplication and Division (from left to right)
- Addition and Subtraction (from left to right)
Therefore, we first need to carry out the operations in the parentheses. (If there is an exponent inside the parentheses, this should be done first).
[tex]\sf \dfrac{4^3 \div (-12+2^2)}{(2 \times 3)^2+(-5 \times 2 \times 3)+2}[/tex]
[tex]=\sf \dfrac{4^3 \div (-12+4)}{(2 \times 3)^2+(-5 \times 2 \times 3)+2}[/tex]
[tex]=\sf \dfrac{4^3 \div (-8)}{(6)^2+(-30)+2}[/tex]
Next carry out the exponents:
[tex]=\sf \dfrac{64 \div (-8)}{36+(-30)+2}[/tex]
Next carry out the multiplication and division (there is only a division here):
[tex]=\sf \dfrac{-8}{36+(-30)+2}[/tex]
Next carry out the addition and subtraction, working from left to right:
[tex]=\sf \dfrac{-8}{6+2}[/tex]
[tex]=\sf \dfrac{-8}{8}[/tex]
Finally, simplify:
[tex]=\sf \dfrac{-8}{8}=-1[/tex]
