From the given following which of these operators have the highest order of precedence.Options+' and '-'(' and ')'*' and '/'~' and '^'

To determine which of the given operators has the highest order of precedence, we will analyze the operators listed in conjunction with standard operator precedence rules in mathematics.

1. Break Down the Problem

We have the following operators to analyze for precedence:

1. Addition (+) and Subtraction (-)
2. Parentheses (( and ))
3. Multiplication (*) and Division (/)
4. Unary negation (~) and Exponentiation (^)

2. Relevant Concepts

Operator precedence rules dictate the order in which different types of operations are performed in mathematical expressions:

• Parentheses: Highest precedence; operations within parentheses are done first.
• Exponentiation: Next level of precedence.
• Multiplication and Division: Same level of precedence, performed left to right.
• Addition and Subtraction: Lowest level of precedence, also performed left to right.
• Unary Operations: Unary negation typically takes precedence over the standard binary operations but is often evaluated at its level depending on the context.

3. Analysis and Detail

• Parentheses (( and )) always take the highest precedence, meaning any calculation within parentheses will be completed first.
• Exponentiation (^) follows next and is performed before multiplication and division.
• Multiplication (*) and division (/) share the same level of precedence, which means they are evaluated from left to right.
• Finally, addition (+) and subtraction (-) have the lowest precedence and are performed after multiplication and division.

4. Verify and Summarize

From the above analysis:

1. Parentheses (( and )): Highest precedence
2. Exponentiation (^)
3. Multiplication (*) and Division (/): Same level
4. Addition (+) and Subtraction (-): Lowest level

Final Answer

The operator with the highest order of precedence is Parentheses (( and )).