https://file.aiquickdraw.com/mathbot/file/1726566280330hc2g5ftp.jpg

The expression shown in the image is:

\[
(5a^{-3}b^{-4})(2a^{2}b^{5}) = 10a^{-1}b
\]

### Step-by-step Explanation:

1. **Multiply the constants**:  
   The constants are \(5\) and \(2\). When multiplying these, we get:
   \[
   5 \times 2 = 10
   \]

2. **Add the exponents of \(a\)**:  
   Using the law of exponents, \(a^m \times a^n = a^{m+n}\), we add the exponents of \(a\) in the two terms:
   \[
   a^{-3} \times a^2 = a^{-3+2} = a^{-1}
   \]

3. **Add the exponents of \(b\)**:  
   Similarly, we add the exponents of \(b\):
   \[
   b^{-4} \times b^5 = b^{-4+5} = b^1
   \]

Thus, the simplified form of the expression is:
\[
10a^{-1}b
\]

This matches the given result.

Would you like further details or have any questions?

Here are some related questions for practice:
1. How do you simplify \((3a^5b^2)(4a^{-3}b^{-6})\)?
2. What is the result of \((6x^{-4}y^3)(5x^2y^{-2})\)?
3. Can you simplify \((7c^3d^{-1})(2c^{-5}d^4)\)?
4. How do you apply the power of a product rule to expressions like \((2ab^3)^2\)?
5. What happens when you multiply two terms where one variable has a zero exponent?

**Tip**: Always remember to add exponents when multiplying terms with the same base.

Learn how to simplify the algebraic expression (5a^-3b^-4)(2a^2b^5) by using the laws of exponents. The step-by-step process involves multiplying constants and adding exponents. Suitable for students in Grades 8-10.

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