https://file.aiquickdraw.com/mathbot/file/1725796857373s65z8dqk.jpg

The equation shown in the image is:

\[
\frac{1}{100,000} = 10^x
\]

We need to find the value of \(x\).

### Step-by-Step Solution:

1. **Express the Fraction as a Power of 10:**
   \[
   \frac{1}{100,000} = \frac{1}{10^5}
   \]
   \[
   \frac{1}{10^5} = 10^{-5}
   \]

2. **Set the Equation:**
   \[
   10^{-5} = 10^x
   \]

3. **Compare the Exponents:**
   Since the bases are the same, we can equate the exponents:
   \[
   x = -5
   \]

### Final Answer:
\[
x = -5
\]

Would you like more details or have any questions on this? 

Here are some related questions you might find interesting:

1. What is the general rule for converting a fraction to a power of 10?
2. How can you determine the exponent when dividing numbers in scientific notation?
3. What happens to the exponent when you multiply or divide by a power of 10?
4. How would you solve for \(x\) in the equation \(10^x = 100\)?
5. What is the significance of negative exponents in mathematics?

**Tip:** When working with exponents, always remember that negative exponents indicate reciprocals of the base raised to the corresponding positive exponent.

What is the value of x in the equation 1/100000 = 10^x?

Learn how to solve the equation 1/100000 = 10^x using exponent rules. This problem involves simplifying a fraction as a power of 10 and solving for x. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation