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The problem you have shared asks to find the value of \( n \) in the equation:

\[
1.9 \times 10^n = (1 \times 10^5)(1.9 \times 10^{17})
\]

Let's solve this step-by-step:

### Step 1: Multiply the terms on the right-hand side

\[
(1 \times 10^5) \times (1.9 \times 10^{17})
\]

Using the rules of exponents:

\[
1 \times 1.9 = 1.9
\]
\[
10^5 \times 10^{17} = 10^{5+17} = 10^{22}
\]

So, the right-hand side becomes:

\[
1.9 \times 10^{22}
\]

### Step 2: Set the equation equal

Now we have the equation:

\[
1.9 \times 10^n = 1.9 \times 10^{22}
\]

Since the coefficients (1.9) are the same on both sides, we can equate the exponents:

\[
n = 22
\]

### Final Answer:
The value of \( n \) is \( 22 \).

---

Do you want further details or have any questions?

Here are some related questions you could explore:
1. How do you multiply powers of 10 with different exponents?
2. What are the rules for adding exponents in scientific notation?
3. How does scientific notation help simplify large number calculations?
4. Can you solve a similar equation with different bases?
5. How would the solution change if the coefficient on one side was different?

**Tip:** When multiplying numbers in scientific notation, always deal with the coefficients and the powers of 10 separately.

What is the value of n in the equation 1.9 × 10^n = (1 × 10^5)(1.9 × 10^17)?

Learn how to solve for n in the scientific notation equation 1.9 × 10^n = (1 × 10^5)(1.9 × 10^17) using exponent rules. This problem focuses on multiplying powers of 10 and is suitable for high school students in Grades 9-12.

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