Question

1. modeling real life

a microscope magnifies an object (10^5) times. the length of an object is (10^{-7}) meter. what is its magnified length?

Explanation:

Step1: Recall exponent rule for multiplication

To find the magnified length, we multiply the original length by the magnification factor. The rule for multiplying exponents with the same base is \(a^m \times a^n = a^{m + n}\). Here, the original length is \(10^{-7}\) meters and the magnification is \(10^{5}\), so we calculate \(10^{-7} \times 10^{5}\).

Step2: Apply the exponent rule

Using the rule \(a^m \times a^n = a^{m + n}\), we have \(10^{-7 + 5}=10^{-2}\).

Step3: Convert to decimal form (optional, but clear)

We know that \(10^{-2}=\frac{1}{10^{2}}=\frac{1}{100} = 0.01\) meters. But we can also leave it in scientific notation as \(10^{-2}\) meters.

Answer:

The magnified length is \(10^{-2}\) meters (or \(0.01\) meters).