Evaluate The Expression:$\left(8 \times 10^6\right) \div \left(4 \times 10^3\right$\]

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Introduction

In mathematics, evaluating expressions is a crucial skill that helps us simplify complex mathematical problems. It involves applying the order of operations (PEMDAS) to break down the expression into manageable parts and then solving it step by step. In this article, we will evaluate the expression $\left(8 \times 10^6\right) \div \left(4 \times 10^3\right)$ using the order of operations and provide a step-by-step guide to simplify it.

Understanding the Order of Operations

Before we dive into evaluating the expression, it's essential to understand the order of operations, which is a set of rules that tells us which operations to perform first when there are multiple operations in an expression. The order of operations is often remembered using the acronym PEMDAS, which stands for:

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 Expression

Now that we understand the order of operations, let's apply it to the given expression:

$\left(8 \times 10^6\right) \div \left(4 \times 10^3\right)$

Step 1: Evaluate Expressions Inside Parentheses

The expression inside the parentheses is already simplified, so we can move on to the next step.

Step 2: Evaluate Exponential Expressions

The expression contains two exponential terms: $10^6$ and $10^3$. We can evaluate these expressions by raising 10 to the power of 6 and 3, respectively.

$10^6 = 1,000,000$

$10^3 = 1,000$

Step 3: Multiply and Divide from Left to Right

Now that we have evaluated the exponential expressions, we can multiply and divide from left to right.

$\left(8 \times 1,000,000\right) \div \left(4 \times 1,000\right)$

$= 8,000,000 \div 4,000$

Step 4: Simplify the Expression

Finally, we can simplify the expression by dividing 8,000,000 by 4,000.

$= 2,000$

Conclusion

Evaluating the expression $\left(8 \times 10^6\right) \div \left(4 \times 10^3\right)$ using the order of operations involves breaking down the expression into manageable parts and then solving it step by step. By following the order of operations (PEMDAS), we can simplify complex mathematical expressions and arrive at the correct solution.

Frequently Asked Questions

Q: What is the order of operations?

A: The order of operations is a set of rules that tells us which operations to perform first when there are multiple operations in an expression. The order of operations is often remembered using the acronym PEMDAS, which stands for:

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.

Q: How do I evaluate exponential expressions?

A: To evaluate exponential expressions, you need to raise the base number to the power of the exponent. For example, $10^6 = 1,000,000$.

Q: What is the final answer to the expression?

A: The final answer to the expression $\left(8 \times 10^6\right) \div \left(4 \times 10^3\right)$ is 2,000.

Additional Resources

If you want to learn more about evaluating expressions and the order of operations, here are some additional resources:

• Khan Academy: Order of Operations
• Mathway: Order of Operations
• Wolfram Alpha: Order of Operations

By following the steps outlined in this article and using the order of operations, you can simplify complex mathematical expressions and arrive at the correct solution.