Simplify The Expression: ${ \frac{3^3 - (\sqrt{4})^2 + \sqrt[3]{-64}}{-4^2 \times 1^3 + 17} }$

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Introduction

In this article, we will simplify the given mathematical expression step by step. The expression involves various mathematical operations such as exponentiation, square root, cube root, and arithmetic operations. Our goal is to simplify the expression to its simplest form.

The Given Expression

The given expression is:

{ \frac{3^3 - (\sqrt{4})^2 + \sqrt[3]{-64}}{-4^2 \times 1^3 + 17} \}

Step 1: Evaluate the Exponents

The first step is to evaluate the exponents in the expression.

  • 333^3 is equal to 3×3×3=273 \times 3 \times 3 = 27
  • (4)2(\sqrt{4})^2 is equal to 4×4=2×2=4\sqrt{4} \times \sqrt{4} = 2 \times 2 = 4
  • −42-4^2 is equal to −(4×4)=−16- (4 \times 4) = -16
  • 131^3 is equal to 1×1×1=11 \times 1 \times 1 = 1

Step 2: Simplify the Expression

Now that we have evaluated the exponents, we can simplify the expression.

{ \frac{27 - 4 + \sqrt[3]{-64}}{-16 \times 1 + 17} \}

Step 3: Evaluate the Cube Root

The next step is to evaluate the cube root in the expression.

  • −643\sqrt[3]{-64} is equal to −4-4 because −4×−4×−4=−64-4 \times -4 \times -4 = -64

Step 4: Simplify the Expression Further

Now that we have evaluated the cube root, we can simplify the expression further.

{ \frac{27 - 4 - 4}{-16 + 17} \}

Step 5: Perform Arithmetic Operations

The final step is to perform the arithmetic operations in the expression.

  • 27−4−4=1927 - 4 - 4 = 19
  • −16+17=1-16 + 17 = 1

Step 6: Simplify the Expression to Its Final Form

Now that we have performed the arithmetic operations, we can simplify the expression to its final form.

{ \frac{19}{1} = 19 \}

Conclusion

In this article, we simplified the given mathematical expression step by step. We evaluated the exponents, simplified the expression, evaluated the cube root, simplified the expression further, performed the arithmetic operations, and finally simplified the expression to its final form.

Frequently Asked Questions

Q: What is the final simplified form of the expression?

A: The final simplified form of the expression is 19.

Q: What is the process of simplifying a mathematical expression?

A: The process of simplifying a mathematical expression involves evaluating exponents, simplifying the expression, evaluating cube roots, simplifying the expression further, performing arithmetic operations, and finally simplifying the expression to its final form.

Q: What are the common mathematical operations involved in simplifying an expression?

A: The common mathematical operations involved in simplifying an expression include exponentiation, square root, cube root, and arithmetic operations such as addition, subtraction, multiplication, and division.

Final Thoughts

Simplifying a mathematical expression can be a challenging task, but by breaking it down into smaller steps and following a systematic approach, we can simplify even the most complex expressions. In this article, we simplified the given expression step by step, and the final simplified form of the expression is 19.

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Introduction

In our previous article, we simplified the given mathematical expression step by step. In this article, we will answer some frequently asked questions related to simplifying mathematical expressions.

Q&A

Q: What is the process of simplifying a mathematical expression?

A: The process of simplifying a mathematical expression involves evaluating exponents, simplifying the expression, evaluating cube roots, simplifying the expression further, performing arithmetic operations, and finally simplifying the expression to its final form.

Q: What are the common mathematical operations involved in simplifying an expression?

A: The common mathematical operations involved in simplifying an expression include exponentiation, square root, cube root, and arithmetic operations such as addition, subtraction, multiplication, and division.

Q: How do I evaluate exponents in a mathematical expression?

A: To evaluate exponents in a mathematical expression, you need to multiply the base number by itself as many times as the exponent indicates. For example, 333^3 is equal to 3×3×3=273 \times 3 \times 3 = 27.

Q: How do I simplify a mathematical expression with a cube root?

A: To simplify a mathematical expression with a cube root, you need to find the cube root of the number inside the cube root symbol. For example, −643\sqrt[3]{-64} is equal to −4-4 because −4×−4×−4=−64-4 \times -4 \times -4 = -64.

Q: What is the difference between a square root and a cube root?

A: A square root is a mathematical operation that involves finding the number that, when multiplied by itself, gives the original number. A cube root is a mathematical operation that involves finding the number that, when multiplied by itself three times, gives the original number.

Q: How do I simplify a mathematical expression with multiple operations?

A: To simplify a mathematical expression with multiple operations, you need to follow the order of operations (PEMDAS):

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

Q: What are some common mistakes to avoid when simplifying a mathematical expression?

A: Some common mistakes to avoid when simplifying a mathematical expression include:

  • Not following the order of operations (PEMDAS)
  • Not evaluating exponents correctly
  • Not simplifying the expression further after evaluating exponents and cube roots
  • Not performing arithmetic operations correctly

Conclusion

In this article, we answered some frequently asked questions related to simplifying mathematical expressions. We covered topics such as the process of simplifying a mathematical expression, common mathematical operations involved in simplifying an expression, evaluating exponents, simplifying expressions with cube roots, and common mistakes to avoid.

Final Thoughts

Simplifying a mathematical expression can be a challenging task, but by following a systematic approach and avoiding common mistakes, we can simplify even the most complex expressions. In this article, we provided some tips and guidelines to help you simplify mathematical expressions with confidence.

Additional Resources

If you want to learn more about simplifying mathematical expressions, here are some additional resources you can check out:

  • Khan Academy: Simplifying Expressions
  • Mathway: Simplifying Expressions
  • Wolfram Alpha: Simplifying Expressions

Frequently Asked Questions

Q: What is the final simplified form of the expression?

A: The final simplified form of the expression is 19.

Q: What is the process of simplifying a mathematical expression?

A: The process of simplifying a mathematical expression involves evaluating exponents, simplifying the expression, evaluating cube roots, simplifying the expression further, performing arithmetic operations, and finally simplifying the expression to its final form.

Q: What are the common mathematical operations involved in simplifying an expression?

A: The common mathematical operations involved in simplifying an expression include exponentiation, square root, cube root, and arithmetic operations such as addition, subtraction, multiplication, and division.

Final Answer

The final answer to the given expression is 19.