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The problem states that a camera lens magnifies an object **\(10^7\)** times, and the original length of the object is **\(10^{-7}\)** centimeters. We are asked to find the magnified length.

To solve this:

- The magnified length \( L_{\text{magnified}} \) is given by:
\[
L_{\text{magnified}} = \text{magnification factor} \times L_{\text{original}}
\]
\[
L_{\text{magnified}} = 10^7 \times 10^{-7} \, \text{cm}
\]
- When multiplying these powers of 10:
\[
L_{\text{magnified}} = 10^0 = 1 \, \text{cm}
\]

Thus, the magnified length of the object is **1 centimeter**.

Would you like further details or have any questions?

Here are 5 related questions for further exploration:
1. What happens to the magnified length if the magnification factor is doubled?
2. How would the magnified length change if the original length was \(10^{-6}\) cm?
3. How do we calculate the magnification of a lens given the object and image distance?
4. What is the relationship between magnification and resolution in optical systems?
5. How would a magnification factor of \(10^{-7}\) affect a different object?

**Tip:** When dealing with powers of 10, multiplication and division simplify through the addition or subtraction of the exponents.

A camera lens magnifies an object 10^7 times. The length of an object is 10^-7 centimeter. What is its magnified length?

Learn how to calculate the magnified length of an object using the magnification factor and exponents. This problem covers key concepts such as the multiplication of powers of 10 and is suitable for students in Grades 9-10.

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