Simplify The Expression:$(-2)^3 - 3 \times (-3) \times 2^2$

Introduction

In this article, we will simplify the given mathematical expression: $(-2)^3 - 3 \times (-3) \times 2^2$. We will break down the expression into smaller parts, apply the order of operations, and simplify each part to arrive at the final result.

Understanding the Expression

The given expression is a combination of exponents, multiplication, and subtraction. To simplify it, we need to follow the order of operations, which is a set of rules that dictate the order in which we perform mathematical operations.

The expression can be broken down into three main parts:

1. $(-2)^3$
2. $3 \times (-3)$
3. $2^2$

Simplifying the Exponents

Let's start by simplifying the exponents.

Simplifying $(-2)^3$

To simplify $(-2)^3$, we need to apply the exponent rule, which states that $(a^m)^n = a^{m \times n}$. In this case, $a = -2$ and $m = 3$.

$(-2)^3 = (-2) \times (-2) \times (-2) = -8$

Simplifying $2^2$

To simplify $2^2$, we need to apply the exponent rule, which states that $a^m = a \times a \times ... \times a$ (m times). In this case, $a = 2$ and $m = 2$.

$2^2 = 2 \times 2 = 4$

Simplifying the Multiplication

Now that we have simplified the exponents, let's simplify the multiplication.

Simplifying $3 \times (-3)$

To simplify $3 \times (-3)$, we need to multiply the two numbers.

$3 \times (-3) = -9$

Substituting the Simplified Values

Now that we have simplified the exponents and the multiplication, let's substitute the simplified values back into the original expression.

$(-2)^3 - 3 \times (-3) \times 2^2 = -8 - (-9) \times 4$

Simplifying the Expression

Now that we have substituted the simplified values, let's simplify the expression.

$-8 - (-9) \times 4 = -8 + 36 = 28$

Conclusion

In this article, we simplified the given mathematical expression: $(-2)^3 - 3 \times (-3) \times 2^2$. We broke down the expression into smaller parts, applied the order of operations, and simplified each part to arrive at the final result.

Key Takeaways

• To simplify a mathematical expression, we need to follow the order of operations.
• Exponents should be simplified first, followed by multiplication and subtraction.
• We can use the exponent rule to simplify expressions with exponents.
• We can use the multiplication rule to simplify expressions with multiplication.

Final Answer

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Introduction

In our previous article, we simplified the given mathematical expression: $(-2)^3 - 3 \times (-3) \times 2^2$. We broke down the expression into smaller parts, applied the order of operations, and simplified each part to arrive at the final result.

In this article, we will answer some frequently asked questions related to simplifying mathematical expressions. We will cover topics such as exponents, multiplication, and the order of operations.

Q&A

Q: What is the order of operations?

A: The order of operations is a set of rules that dictate the order in which we perform mathematical operations. The order of operations is:

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

Q: How do I simplify expressions with exponents?

A: To simplify expressions with exponents, you can use the exponent rule, which states that $(a^m)^n = a^{m \times n}$. For example, to simplify $(-2)^3$, you can apply the exponent rule as follows:

$(-2)^3 = (-2) \times (-2) \times (-2) = -8$

Q: How do I simplify expressions with multiplication?

A: To simplify expressions with multiplication, you can multiply the numbers together. For example, to simplify $3 \times (-3)$, you can multiply the numbers together as follows:

$3 \times (-3) = -9$

Q: What is the difference between $(-2)^3$ and $-2^3$?

A: The difference between $(-2)^3$ and $-2^3$ is the order of operations. In $(-2)^3$, the exponent is evaluated first, and then the result is multiplied by $-1$. In $-2^3$, the exponent is evaluated first, and then the result is multiplied by $-1$.

$(-2)^3 = (-2) \times (-2) \times (-2) = -8$

$-2^3 = -(2 \times 2 \times 2) = -8$

Q: How do I simplify expressions with multiple operations?

A: To simplify expressions with multiple operations, you can follow the order of operations. For example, to simplify $(-2)^3 - 3 \times (-3) \times 2^2$, you can follow the order of operations as follows:

1. Simplify the exponents: $(-2)^3 = -8$ and $2^2 = 4$
2. Simplify the multiplication: $3 \times (-3) = -9$
3. Substitute the simplified values back into the original expression: $-8 - (-9) \times 4$
4. Simplify the expression: $-8 + 36 = 28$

Conclusion

In this article, we answered some frequently asked questions related to simplifying mathematical expressions. We covered topics such as exponents, multiplication, and the order of operations.

Key Takeaways

• The order of operations is a set of rules that dictate the order in which we perform mathematical operations.
• Exponents should be simplified first, followed by multiplication and subtraction.
• We can use the exponent rule to simplify expressions with exponents.
• We can use the multiplication rule to simplify expressions with multiplication.

Final Answer

The final answer is: $\boxed{28}$