Evaluate The Expression: ${ (5-2)^3 + (13-8)^3 \times 5 }$

Introduction

In this article, we will evaluate the given mathematical expression: $(5-2)^3 + (13-8)^3 \times 5$. This expression involves basic arithmetic operations such as subtraction, exponentiation, and multiplication. We will break down the expression step by step, simplifying it at each stage until we arrive at the final result.

Step 1: Evaluate the Expressions Inside the Parentheses

The given expression is $(5-2)^3 + (13-8)^3 \times 5$. To start, we need to evaluate the expressions inside the parentheses. Let's begin with the first expression: $(5-2)^3$.

(5-2)^3 = (3)^3 = 27

Next, we will evaluate the second expression: $(13-8)^3$.

(13-8)^3 = (5)^3 = 125

Step 2: Multiply the Second Expression by 5

Now that we have evaluated the expressions inside the parentheses, we can proceed to multiply the second expression by 5.

(13-8)^3 \times 5 = 125 \times 5 = 625

Step 3: Add the Results of the Two Expressions

Finally, we will add the results of the two expressions: $(5-2)^3$ and $(13-8)^3 \times 5$.

(5-2)^3 + (13-8)^3 \times 5 = 27 + 625 = 652

Conclusion

In this article, we evaluated the given mathematical expression: $(5-2)^3 + (13-8)^3 \times 5$. We broke down the expression step by step, simplifying it at each stage until we arrived at the final result. The final answer is $\boxed{652}$.

Frequently Asked Questions

Q: What is the order of operations in the given expression? A: The order of operations in the given expression is: subtraction, exponentiation, multiplication, and addition.

Q: How do we evaluate the expressions inside the parentheses? A: We evaluate the expressions inside the parentheses by following the order of operations: subtraction, exponentiation, and multiplication.

Q: What is the final result of the given expression? A: The final result of the given expression is 652.

Final Answer

The final answer is $\boxed{652}$.

Introduction

In our previous article, we evaluated the given mathematical expression: $(5-2)^3 + (13-8)^3 \times 5$. We broke down the expression step by step, simplifying it at each stage until we arrived at the final result. In this article, we will provide a Q&A section to address any questions or concerns that readers may have.

Q&A

Q: What is the order of operations in the given expression?

A: The order of operations in the given expression is: subtraction, exponentiation, multiplication, and addition. This is often remembered using the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Q: How do we evaluate the expressions inside the parentheses?

A: We evaluate the expressions inside the parentheses by following the order of operations: subtraction, exponentiation, and multiplication. For example, in the expression $(5-2)^3$, we first evaluate the expression inside the parentheses: $5-2=3$. Then, we raise 3 to the power of 3: $3^3=27$.

Q: What is the difference between exponentiation and multiplication?

A: Exponentiation and multiplication are two different operations. Exponentiation involves raising a number to a power, while multiplication involves multiplying two numbers together. For example, in the expression $(5-2)^3$, we are raising the result of the subtraction to the power of 3, not multiplying 5 and 2 together.

Q: Can you explain the concept of exponentiation?

A: Exponentiation is a mathematical operation that involves raising a number to a power. For example, $2^3$ means 2 raised to the power of 3, which is equal to 2 multiplied by itself 3 times: $2 \times 2 \times 2 = 8$. Exponentiation is often used to represent repeated multiplication.

Q: How do we handle negative numbers in exponentiation?

A: When a negative number is raised to a power, the result is always positive. For example, $(-2)^3$ means -2 raised to the power of 3, which is equal to -2 multiplied by itself 3 times: $-2 \times -2 \times -2 = -8$.

Q: Can you explain the concept of multiplication?

A: Multiplication is a mathematical operation that involves multiplying two numbers together. For example, $2 \times 3$ means 2 multiplied by 3, which is equal to 6. Multiplication is often used to represent repeated addition.

Q: How do we handle fractions in multiplication?

A: When a fraction is multiplied by a number, the result is a new fraction. For example, $\frac{1}{2} \times 3$ means $\frac{1}{2}$ multiplied by 3, which is equal to $\frac{3}{2}$.

Q: Can you explain the concept of addition?

A: Addition is a mathematical operation that involves combining two or more numbers together. For example, $2 + 3$ means 2 added to 3, which is equal to 5. Addition is often used to represent the total amount of something.

Q: How do we handle negative numbers in addition?

A: When a negative number is added to a positive number, the result is always negative. For example, $2 + (-3)$ means 2 added to -3, which is equal to -1.

Conclusion

In this article, we provided a Q&A section to address any questions or concerns that readers may have about the given mathematical expression: $(5-2)^3 + (13-8)^3 \times 5$. We explained various mathematical concepts, including exponentiation, multiplication, and addition, and provided examples to illustrate each concept.

Final Answer

The final answer is $\boxed{652}$.