Evaluate The Expression $36+5^3$. $36+5^3=$

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Introduction

In mathematics, expressions are a combination of numbers, variables, and mathematical operations. Evaluating an expression involves substituting values for variables and performing the operations to obtain a numerical value. In this article, we will evaluate the expression 36+5336+5^3.

Understanding the Expression

The given expression is 36+5336+5^3. To evaluate this expression, we need to follow the order of operations (PEMDAS):

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  3. Multiplication and Division: Evaluate multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Evaluating the Exponential Expression

The expression 535^3 is an exponential expression. To evaluate this expression, we need to raise 5 to the power of 3.

Raising 5 to the Power of 3

To raise 5 to the power of 3, we need to multiply 5 by itself three times:

53=5×5×5=1255^3 = 5 \times 5 \times 5 = 125

Evaluating the Expression

Now that we have evaluated the exponential expression, we can substitute the value into the original expression:

36+53=36+12536+5^3 = 36+125

Performing Addition

The final step is to perform the addition operation:

36+125=16136+125 = 161

Conclusion

In this article, we evaluated the expression 36+5336+5^3. We followed the order of operations (PEMDAS) and evaluated the exponential expression 535^3 first. We then substituted the value into the original expression and performed the addition operation to obtain the final result: 161161.

Tips and Tricks

  • When evaluating expressions, always follow the order of operations (PEMDAS).
  • Evaluate exponential expressions first.
  • Substitute values into the original expression and perform the operations to obtain the final result.

Real-World Applications

Evaluating expressions is a fundamental concept in mathematics and has numerous real-world applications. For example, in finance, evaluating expressions is used to calculate interest rates and investment returns. In science, evaluating expressions is used to model complex systems and make predictions.

Common Mistakes

  • Failing to follow the order of operations (PEMDAS).
  • Not evaluating exponential expressions first.
  • Not substituting values into the original expression and performing the operations to obtain the final result.

Final Thoughts

Evaluating expressions is a critical skill in mathematics and has numerous real-world applications. By following the order of operations (PEMDAS) and evaluating exponential expressions first, we can obtain accurate results. Remember to substitute values into the original expression and perform the operations to obtain the final result.

Frequently Asked Questions

  • Q: What is the order of operations (PEMDAS)? A: The order of operations (PEMDAS) is a set of rules that dictate the order in which mathematical operations should be performed.
  • Q: How do I evaluate exponential expressions? A: To evaluate exponential expressions, raise the base number to the power of the exponent.
  • Q: What is the final result of the expression 36+5336+5^3? A: The final result of the expression 36+5336+5^3 is 161161.

References

Introduction

Evaluating expressions is a fundamental concept in mathematics that has numerous real-world applications. In this article, we will answer some frequently asked questions about evaluating expressions.

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that dictate the order in which mathematical operations should be performed. The acronym PEMDAS stands for:

  • 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.

Q: How do I evaluate exponential expressions?

A: To evaluate exponential expressions, raise the base number to the power of the exponent. For example, to evaluate 535^3, you would multiply 5 by itself three times: 5×5×5=1255 \times 5 \times 5 = 125.

Q: What is the difference between multiplication and division?

A: Multiplication and division are both arithmetic operations that involve combining numbers. However, multiplication involves adding a number a certain number of times, while division involves sharing a number into equal groups.

Q: How do I evaluate expressions with multiple operations?

A: To evaluate expressions with multiple operations, follow the order of operations (PEMDAS). First, evaluate any exponential expressions, then any multiplication and division operations from left to right, and finally any addition and subtraction operations from left to right.

Q: What is the final result of the expression 36+5336+5^3?

A: The final result of the expression 36+5336+5^3 is 161161. To evaluate this expression, we need to follow the order of operations (PEMDAS). First, we evaluate the exponential expression 535^3, which is equal to 125125. Then, we add 3636 and 125125 to get the final result: 161161.

Q: How do I evaluate expressions with variables?

A: To evaluate expressions with variables, substitute a value for the variable and then follow the order of operations (PEMDAS). For example, if we have the expression 2x+52x+5 and we know that x=3x=3, we can substitute 33 for xx and then evaluate the expression: 2(3)+5=112(3)+5=11.

Q: What is the difference between an expression and an equation?

A: An expression is a combination of numbers, variables, and mathematical operations, while an equation is a statement that says two expressions are equal. For example, the expression 2x+52x+5 is a combination of numbers and variables, while the equation 2x+5=112x+5=11 is a statement that says the expression 2x+52x+5 is equal to 1111.

Q: How do I evaluate expressions with fractions?

A: To evaluate expressions with fractions, follow the order of operations (PEMDAS). First, evaluate any exponential expressions, then any multiplication and division operations from left to right, and finally any addition and subtraction operations from left to right. When working with fractions, make sure to simplify the fraction by dividing both the numerator and denominator by their greatest common divisor.

Q: What is the final result of the expression 12+14\frac{1}{2}+\frac{1}{4}?

A: The final result of the expression 12+14\frac{1}{2}+\frac{1}{4} is 34\frac{3}{4}. To evaluate this expression, we need to follow the order of operations (PEMDAS). First, we need to find a common denominator for the two fractions, which is 44. Then, we can add the two fractions: 12+14=24+14=34\frac{1}{2}+\frac{1}{4}=\frac{2}{4}+\frac{1}{4}=\frac{3}{4}.

Q: How do I evaluate expressions with decimals?

A: To evaluate expressions with decimals, follow the order of operations (PEMDAS). First, evaluate any exponential expressions, then any multiplication and division operations from left to right, and finally any addition and subtraction operations from left to right. When working with decimals, make sure to round the result to the correct number of decimal places.

Q: What is the final result of the expression 2.5+1.22.5+1.2?

A: The final result of the expression 2.5+1.22.5+1.2 is 3.73.7. To evaluate this expression, we need to follow the order of operations (PEMDAS). First, we need to add the two decimals: 2.5+1.2=3.72.5+1.2=3.7.

Conclusion

Evaluating expressions is a fundamental concept in mathematics that has numerous real-world applications. By following the order of operations (PEMDAS) and understanding the rules for evaluating exponential expressions, multiplication and division, and addition and subtraction, we can evaluate expressions accurately and efficiently. Remember to substitute values into the original expression and perform the operations to obtain the final result.

Tips and Tricks

  • Always follow the order of operations (PEMDAS).
  • Evaluate exponential expressions first.
  • Substitute values into the original expression and perform the operations to obtain the final result.
  • Simplify fractions by dividing both the numerator and denominator by their greatest common divisor.
  • Round decimal results to the correct number of decimal places.

Final Thoughts

Evaluating expressions is a critical skill in mathematics that has numerous real-world applications. By following the order of operations (PEMDAS) and understanding the rules for evaluating exponential expressions, multiplication and division, and addition and subtraction, we can evaluate expressions accurately and efficiently. Remember to substitute values into the original expression and perform the operations to obtain the final result.