https://file.aiquickdraw.com/mathbot/file/17263347470300xnq0dm3.jpg

The expression in the image you uploaded appears to be:

\[
\frac{10^{4x + 3}}{10^{3x + 1}} \cdot \frac{10^{2x}}{10^{x - 5}}.
\]

Let's simplify it step by step using the properties of exponents. Recall the following rules:
1. \(\frac{a^m}{a^n} = a^{m - n}\) for division.
2. \(a^m \cdot a^n = a^{m + n}\) for multiplication.

### Step 1: Simplify each fraction
Start with the first fraction:

\[
\frac{10^{4x + 3}}{10^{3x + 1}} = 10^{(4x + 3) - (3x + 1)} = 10^{x + 2}.
\]

Next, simplify the second fraction:

\[
\frac{10^{2x}}{10^{x - 5}} = 10^{2x - (x - 5)} = 10^{x + 5}.
\]

### Step 2: Multiply the two simplified terms
Now, multiply the two results:

\[
10^{x + 2} \cdot 10^{x + 5} = 10^{(x + 2) + (x + 5)} = 10^{2x + 7}.
\]

Thus, the final simplified expression is:

\[
10^{2x + 7}.
\]

Would you like more details on this solution or help with further questions?

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Here are 5 related questions you might find useful:
1. How would you simplify \(\frac{10^{3x+5}}{10^{x+2}}\)?
2. What happens if you encounter terms with different bases, like \(\frac{2^{3x}}{5^{2x}}\)?
3. Can you expand and simplify \((10^{x+3})^2\)?
4. How do logarithms relate to these types of exponential simplifications?
5. What are some real-world applications of these exponent rules in fields like engineering?

### Tip:
When simplifying exponents, always look for common bases to apply exponent rules more easily.

Simplify the expression: (10^(4x+3) / 10^(3x+1)) * (10^(2x) / 10^(x-5))

Learn how to simplify an expression involving exponents, (10^(4x+3) / 10^(3x+1)) * (10^(2x) / 10^(x-5)), using exponent rules. This problem covers key algebraic concepts and is suitable for students in Grades 9-11.

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