Divide.${ \frac{1 \times 10^9}{5 \times 10^{-8}} }$A. ${ 7 \times 10^{16}\$} B. ${ 2 \times 10^{16}\$} C. ${ 3 \times 10^{16}\$} D. ${ 1 \times 10^{16}\$}

Introduction

When dealing with large exponents in division, it's essential to understand the rules of exponentiation and how to simplify complex expressions. In this article, we will delve into the world of large exponents and explore the concept of dividing numbers with exponents. We will use the given problem as a case study to demonstrate the step-by-step process of solving large exponents in division.

The Problem

The problem requires us to divide the number $1 \times 10^9$ by $5 \times 10^{-8}$. To solve this problem, we need to understand the rules of exponentiation and how to simplify complex expressions.

Understanding Exponents

Exponents are a shorthand way of representing repeated multiplication. For example, $2^3$ can be written as $2 \times 2 \times 2$. When we have a number with an exponent, such as $10^9$, it means that the base number (10) is multiplied by itself 9 times.

Simplifying Complex Expressions

To simplify complex expressions, we need to understand the rules of exponentiation. The rules of exponentiation state that:

• When we multiply two numbers with the same base, we add their exponents.
• When we divide two numbers with the same base, we subtract their exponents.
• When we raise a number with an exponent to another power, we multiply the exponents.

Solving the Problem

To solve the problem, we need to divide the number $1 \times 10^9$ by $5 \times 10^{-8}$. We can start by simplifying the expression using the rules of exponentiation.

\frac{1 \times 10^9}{5 \times 10^{-8}} = \frac{1}{5} \times \frac{10^<br/> # Divide: A Comprehensive Guide to Solving Large Exponents in Division

Q&A: Frequently Asked Questions About Dividing Large Exponents

Q: What is the rule for dividing numbers with exponents?

A: When dividing numbers with exponents, we subtract the exponents. For example, $\frac{10^9}{10^8} = 10^{9-8} = 10^1$.

Q: How do I simplify complex expressions with large exponents?

A: To simplify complex expressions with large exponents, we need to understand the rules of exponentiation. We can start by simplifying the expression using the rules of exponentiation, and then we can use the properties of exponents to simplify further.

Q: What is the difference between multiplying and dividing numbers with exponents?

A: When multiplying numbers with exponents, we add the exponents. For example, $10^9 \times 10^8 = 10^{9+8} = 10^{17}$. When dividing numbers with exponents, we subtract the exponents. For example, $\frac{10^9}{10^8} = 10^{9-8} = 10^1$.

Q: How do I handle negative exponents when dividing numbers?

A: When dividing numbers with negative exponents, we can rewrite the expression using the rule that $a^{-n} = \frac{1}{a^n}$. For example, $\frac{10^{-8}}{10^9} = \frac{1}{10^8} \times \frac{1}{10^9} = \frac{1}{10^{8+9}} = \frac{1}{10^{17}}$.

Q: Can I simplify expressions with large exponents using a calculator?

A: Yes, you can simplify expressions with large exponents using a calculator. However, it's essential to understand the rules of exponentiation and how to simplify complex expressions before using a calculator.

Q: What are some common mistakes to avoid when dividing numbers with exponents?

A: Some common mistakes to avoid when dividing numbers with exponents include:

• Forgetting to subtract the exponents
• Not simplifying the expression using the rules of exponentiation
• Not handling negative exponents correctly

Q: How do I check my work when dividing numbers with exponents?

A: To check your work when dividing numbers with exponents, you can:

• Simplify the expression using the rules of exponentiation
• Use the properties of exponents to simplify further
• Check your answer by plugging it back into the original expression

Q: Can I use the order of operations when dividing numbers with exponents?

A: Yes, you can use the order of operations when dividing numbers with exponents. The order of operations states that we should perform operations in the following order:

1. Parentheses
2. Exponents
3. Multiplication and Division (from left to right)
4. Addition and Subtraction (from left to right)

Conclusion

Dividing numbers with large exponents can be challenging, but with practice and patience, you can become proficient in simplifying complex expressions. Remember to understand the rules of exponentiation, handle negative exponents correctly, and check your work to ensure accuracy. By following these tips and practicing regularly, you can become a master of dividing numbers with large exponents.

Final Answer

The final answer to the problem is:

$$\frac{1 \times 10^9}{5 \times 10^{-8}} = \frac{1}{5} \times 10^{9-(-8)} = \frac{1}{5} \times 10^{17} = 2 \times 10^{16} </span></p> <p>The correct answer is B. <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn><mo>×</mo><msup><mn>10</mn><mn>16</mn></msup></mrow><annotation encoding="application/x-tex">2 \times 10^{16}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">2</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8141em;"></span><span class="mord">1</span><span class="mord"><span class="mord">0</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">16</span></span></span></span></span></span></span></span></span></span></span></span>.</p>$$