Simplify the expression using the order of operations.
-$$\frac { 6 + ( - 4 ) ^ { 2 } + 2 \cdot 2 ^ { 2 } } { 2 ^ { 2 } \cdot ( 5 - 3 ) }$$
A)20
B)15
C)0
D)2 7 4

Question

Quizplus · Accepted Answer

Following the order of operations (PEMDAS/BODMAS), we first solve the expressions inside the parentheses, then exponents, followed by multiplication and division (from left to right), and finally addition and subtraction (from left to right). 1. Inside the parentheses: $ ( - 4 ) ^ { 2 } = 16 $ and $ ( 5 - 3 ) = 2 $2. Exponents: $ 2 ^ { 2 } = 4 $ in both the numerator and denominator.3. Multiplication: In the numerator, $ 2 \cdot 2 ^ { 2 } = 2 \cdot 4 = 8 $ and in the denominator, $ 2 ^ { 2 } \cdot ( 5 - 3 ) = 4 \cdot 2 = 8 $.4. The numerator simplifies to $ 6 + 16 + 8 = 30 $.5. The denominator simplifies to $ 8 $.6. Dividing the numerator by the denominator gives $ \frac { 30 } { 8 } = 3.75 $, but since there's a mistake in the calculation process, let's correct it:Correct calculation:- The numerator simplifies to $ 6 + 16 + 8 = 30 $.- The denominator simplifies to $ 4 \cdot 2 = 8 $.- Dividing the numerator by the denominator gives $ \frac { 30 } { 8 } = 3.75 $, but actually, the correct division should be $ \frac { 30 } { 8 } = 15 $ when correctly calculating $ \frac { 30 } { 2 } $ instead, indicating a mistake in the final division step.Correctly following the order of operations:1. $ ( - 4 ) ^ { 2 } = 16 $2. $ 2 \cdot 2 ^ { 2 } = 8 $3. $ 2 ^ { 2 } = 4 $4. Numerator: $ 6 + 16 + 8 = 30 $5. Denominator: $ 4 \cdot 2 = 8 $6. Simplifying: $ \frac { 30 } { 8 } $ should correctly simplify based on the given options, indicating a mistake in the explanation process.Given the options and the calculation mistake, none of the provided steps lead to the options given, suggesting a recalculation is necessary:Recalculation without error:- Numerator: $ 6 + 16 + 8 = 30 $- Denominator: $ 4 \cdot 2 = 8 $- Correct division: $ \frac { 30 } { 8 } = 3.75 $, which does not match any of the options, indicating a fundamental error in the interpretation of the options.The correct step-by-step calculation without errors should lead to an answer that matches one of the provided options, but the explanation given contains a mistake in the final division or interpretation of the options. The correct answer should be recalculated based on the order of operations accurately.

Simplify the Expression Using the Order of Operations 6+(−4)2+2⋅2222⋅(5−3)\frac { 6 + ( - 4 ) ^ { 2 } + 2 \cdot 2 ^ { 2 } } { 2 ^ { 2 } \cdot ( 5 - 3 ) }22⋅(5−3)6+(−4)2+2⋅22​

Simplify the Expression Using the Order of Operations $\frac { 6 + ( - 4 ) ^ { 2 } + 2 \cdot 2 ^ { 2 } } { 2 ^ { 2 } \cdot ( 5 - 3 ) }$