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Zorluk: OrtaOrder of Operations and Number Properties

What is the integer value of the expression 42+15÷3×2(3)3-4^2 + | -15 \div 3 \times 2 | - (-3)^3?

Cevap: 21

Cevap

The correct answer is 21.
The correct answer is obtained by strictly following the order of operations (PEMDAS): first evaluating exponents (42=16-4^2 = -16 and (3)3=27(-3)^3 = -27), then performing the operations inside the absolute value from left to right (15÷3=5-15 \div 3 = -5 followed by 5×2=10-5 \times 2 = -10, which simplifies to 10=10|-10| = 10), and finally executing addition and subtraction from left to right (16+10(27)=21-16 + 10 - (-27) = 21).

Adım Adım Çözüm

1
Evaluate the exponent 42-4^2
16-16
According to the order of operations, the exponent is applied to the base 4 first, and then the negation is applied, yielding (42)=16-(4^2) = -16.
2
Evaluate the absolute value expression 15÷3×2|-15 \div 3 \times 2|
1010
Multiplication and division have the same precedence and must be performed from left to right: first 15÷3=5-15 \div 3 = -5, then 5×2=10-5 \times 2 = -10. Taking the absolute value of 10-10 yields 1010.
3
Evaluate the exponent (3)3(-3)^3
27-27
Since the negative sign is inside the parentheses, the base is 3-3, so (3)3=(3)×(3)×(3)=27(-3)^3 = (-3) \times (-3) \times (-3) = -27.
4
Combine the values and simplify
2121
Substitute the evaluated parts into the original expression: 16+10(27)-16 + 10 - (-27). Simplify by performing addition and subtraction from left to right: 16+10=6-16 + 10 = -6, and 6(27)=6+27=21-6 - (-27) = -6 + 27 = 21.

Anahtar Kavram

Order of operations (PEMDAS) and absolute value properties
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