Answer:
-25
Step-by-step explanation:
PEMDAS
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)
Given expression:
[tex]\sf \dfrac{(20-5^2)(16+2^2)}{-2^3+(3 \times 2^2)}[/tex]
As the given expression is a fraction, carry out the operations in the numerator and denominator first before finally dividing them.
Following PEMDAS, carry out the calculations inside the parentheses first, then carry out the rest of the calculations following the order of operations:
Parentheses
Calculate the exponents inside the parentheses:
[tex]\implies \sf \dfrac{(20-25)(16+4)}{-2^3+(3 \times 4)}[/tex]
Multiply:
[tex]\implies \sf \dfrac{(20-25)(16+4)}{-2^3+(12)}[/tex]
Add and subtract:
[tex]\implies \sf \dfrac{(-5)(20)}{-2^3+(12)}[/tex]
Exponents
Calculate the exponent:
[tex]\implies \sf \dfrac{(-5)(20)}{-8+(12)}[/tex]
Multiply and Divide
Multiply:
[tex]\implies \sf \dfrac{-100}{-8+(12)}[/tex]
Add and Subtract
Add:
[tex]\implies \sf \dfrac{-100}{4}[/tex]
Finally, divide the numerator by the denominator:
[tex]\implies \sf -25[/tex]
