Simplify And Solve The Equation: 4 2 + 5 = 6 × ( 2 + 2 4^2 + 5 = 6 \times (2 + 2 4 2 + 5 = 6 × ( 2 + 2 ]

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Introduction

Mathematics is a fundamental subject that deals with numbers, quantities, and shapes. It is a crucial tool for problem-solving, critical thinking, and logical reasoning. In this article, we will simplify and solve the equation 42+5=6×(2+2)4^2 + 5 = 6 \times (2 + 2). This equation involves basic arithmetic operations such as exponentiation, addition, and multiplication.

Understanding the Equation

The given equation is 42+5=6×(2+2)4^2 + 5 = 6 \times (2 + 2). To simplify and solve this equation, we need to follow the order of operations (PEMDAS):

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

Step 1: Evaluate the Expressions Inside the Parentheses

The equation contains an expression inside the parentheses: (2+2)(2 + 2). To evaluate this expression, we need to add 2 and 2.

# Evaluate the expression inside the parentheses
expression = 2 + 2
print(expression)

The output of this expression is 4.

Step 2: Evaluate the Exponential Expression

The equation contains an exponential expression: 424^2. To evaluate this expression, we need to raise 4 to the power of 2.

# Evaluate the exponential expression
exponential_expression = 4 ** 2
print(exponential_expression)

The output of this expression is 16.

Step 3: Multiply 6 by the Result of the Expression Inside the Parentheses

Now that we have evaluated the expression inside the parentheses, we can multiply 6 by the result.

# Multiply 6 by the result of the expression inside the parentheses
result = 6 * 4
print(result)

The output of this expression is 24.

Step 4: Add 5 to the Result of the Exponential Expression

Now that we have evaluated the exponential expression, we can add 5 to the result.

# Add 5 to the result of the exponential expression
result = 16 + 5
print(result)

The output of this expression is 21.

Step 5: Compare the Results

Now that we have evaluated both sides of the equation, we can compare the results.

# Compare the results
if 21 == 24:
    print("The equation is true.")
else:
    print("The equation is false.")

The output of this expression is "The equation is false."

Conclusion

In this article, we simplified and solved the equation 42+5=6×(2+2)4^2 + 5 = 6 \times (2 + 2). We followed the order of operations (PEMDAS) to evaluate the expressions inside the parentheses, the exponential expression, and the multiplication and addition operations. We found that the equation is false.

Frequently Asked Questions

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

A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The acronym PEMDAS stands for:

  • Parentheses: Evaluate the expressions inside the parentheses.
  • Exponents: Evaluate any exponential expressions.
  • Multiplication and Division: Evaluate any 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 an exponential expression?

A: To evaluate an exponential expression, you need to raise the base number to the power of the exponent. For example, to evaluate the expression 424^2, you need to raise 4 to the power of 2.

Q: How do I multiply two numbers?

A: To multiply two numbers, you need to add the first number a number of times equal to the second number. For example, to multiply 6 by 4, you need to add 6 together 4 times.

Q: How do I add two numbers?

A: To add two numbers, you need to combine the two numbers by adding their values. For example, to add 16 and 5, you need to combine their values to get 21.

References

Further Reading

Note: The above article is a rewritten version of the given content in a more readable and SEO-friendly format. The article includes headings, subheadings, and a conclusion. The article also includes frequently asked questions and references for further reading.

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Q&A: Simplify and Solve the Equation 42+5=6×(2+2)4^2 + 5 = 6 \times (2 + 2)

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

A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The acronym PEMDAS stands for:

  • Parentheses: Evaluate the expressions inside the parentheses.
  • Exponents: Evaluate any exponential expressions.
  • Multiplication and Division: Evaluate any 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 an exponential expression?

A: To evaluate an exponential expression, you need to raise the base number to the power of the exponent. For example, to evaluate the expression 424^2, you need to raise 4 to the power of 2.

Q: How do I multiply two numbers?

A: To multiply two numbers, you need to add the first number a number of times equal to the second number. For example, to multiply 6 by 4, you need to add 6 together 4 times.

Q: How do I add two numbers?

A: To add two numbers, you need to combine the two numbers by adding their values. For example, to add 16 and 5, you need to combine their values to get 21.

Q: Why is the equation 42+5=6×(2+2)4^2 + 5 = 6 \times (2 + 2) false?

A: The equation 42+5=6×(2+2)4^2 + 5 = 6 \times (2 + 2) is false because the result of the left-hand side of the equation (21) is not equal to the result of the right-hand side of the equation (24).

Q: What is the difference between the left-hand side and the right-hand side of the equation?

A: The difference between the left-hand side and the right-hand side of the equation is 3. The left-hand side of the equation is 21, and the right-hand side of the equation is 24.

Q: How do I simplify and solve an equation like 42+5=6×(2+2)4^2 + 5 = 6 \times (2 + 2)?

A: To simplify and solve an equation like 42+5=6×(2+2)4^2 + 5 = 6 \times (2 + 2), you need to follow the order of operations (PEMDAS). First, evaluate the expressions inside the parentheses. Then, evaluate any exponential expressions. Next, multiply any numbers together. Finally, add or subtract any numbers together.

Q: What are some common mistakes to avoid when simplifying and solving equations?

A: Some common mistakes to avoid when simplifying and solving equations include:

  • Not following the order of operations (PEMDAS)
  • Not evaluating expressions inside parentheses correctly
  • Not evaluating exponential expressions correctly
  • Not multiplying numbers together correctly
  • Not adding or subtracting numbers together correctly

Conclusion

In this article, we have answered some frequently asked questions about simplifying and solving the equation 42+5=6×(2+2)4^2 + 5 = 6 \times (2 + 2). We have discussed the order of operations (PEMDAS), how to evaluate exponential expressions, how to multiply numbers together, and how to add or subtract numbers together. We have also discussed some common mistakes to avoid when simplifying and solving equations.

Further Reading

References

Note: The above article is a rewritten version of the given content in a more readable and SEO-friendly format. The article includes headings, subheadings, and a conclusion. The article also includes frequently asked questions and references for further reading.