What Is The Value Of This Expression? 42+3×5−(15−3×6)2
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Introduction
In mathematics, expressions are a combination of numbers, variables, and mathematical operations. Evaluating an expression involves performing the operations in the correct order to obtain a result. In this article, we will explore the value of the expression 42+3×5−(15−3×6)2.
Understanding the Order of Operations
The order of operations is a set of rules that dictate the order in which mathematical operations should be performed. The acronym PEMDAS is commonly used to remember the order of operations:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Breaking Down the Expression
Let's break down the expression 42+3×5−(15−3×6)2 into smaller parts to evaluate it step by step.
Step 1: Evaluate the Expression Inside the Parentheses
The expression inside the parentheses is (15−3×6). To evaluate this expression, we need to follow the order of operations.
- Multiply 3 and 6: 3×6 = 18
- Subtract 18 from 15: 15−18 = -3
So, the expression inside the parentheses is -3.
Step 2: Evaluate the Exponential Expression
The expression (15−3×6)2 is an exponential expression. To evaluate this expression, we need to follow the order of operations.
- Evaluate the expression inside the parentheses: -3
- Raise -3 to the power of 2: (-3)2 = 9
So, the exponential expression is 9.
Step 3: Multiply 3 and 5
The expression 3×5 is a multiplication operation. To evaluate this expression, we need to multiply 3 and 5.
- Multiply 3 and 5: 3×5 = 15
Step 4: Add 42 and 15
The expression 42+15 is an addition operation. To evaluate this expression, we need to add 42 and 15.
- Add 42 and 15: 42+15 = 57
Step 5: Subtract 9 from 57
The expression 57−9 is a subtraction operation. To evaluate this expression, we need to subtract 9 from 57.
- Subtract 9 from 57: 57−9 = 48
Conclusion
In conclusion, the value of the expression 42+3×5−(15−3×6)2 is 48. By following the order of operations and breaking down the expression into smaller parts, we can evaluate the expression step by step to obtain the final result.
Frequently Asked Questions
Q: What is the order of operations?
A: The order of operations is a set of rules that dictate the order in which mathematical operations should be performed. The acronym PEMDAS is commonly used to remember the order of operations.
Q: How do I evaluate an expression with parentheses?
A: To evaluate an expression with parentheses, you need to follow the order of operations and evaluate the expression inside the parentheses first.
Q: How do I evaluate an exponential expression?
A: To evaluate an exponential expression, you need to follow the order of operations and raise the base to the power of the exponent.
Q: How do I evaluate a multiplication operation?
A: To evaluate a multiplication operation, you need to multiply the two numbers together.
Q: How do I evaluate an addition operation?
A: To evaluate an addition operation, you need to add the two numbers together.
Q: How do I evaluate a subtraction operation?
A: To evaluate a subtraction operation, you need to subtract the second number from the first number.
Final Answer
The final answer is 48.