https://r2.erweima.ai/mathbot/image/172661277825721skkbvb.jpg

The expression in the image is:

\[
\frac{-2u^2v^1 \times 8u^3v^{-2}}{4u^1v^2}
\]

Let's simplify this step by step.

1. **Simplifying the numerator**:
   \[
   -2u^2v \times 8u^3v^{-2} = (-2 \times 8) u^{2+3} v^{1+(-2)}
   \]
   \[
   = -16u^5v^{-1}
   \]

2. **Simplifying the entire expression**:
   \[
   \frac{-16u^5v^{-1}}{4u^1v^2} = \frac{-16}{4} \times \frac{u^5}{u^1} \times \frac{v^{-1}}{v^2}
   \]
   \[
   = -4u^{5-1}v^{-1-2}
   \]
   \[
   = -4u^4v^{-3}
   \]

3. **Final simplified expression**:
   \[
   -4u^4v^{-3}
   \]
   Alternatively, this could be written as:
   \[
   -4u^4 \times \frac{1}{v^3} = \frac{-4u^4}{v^3}
   \]

Let me know if you'd like more details, or if you have any questions!

Here are five related questions to practice:
1. Simplify: \(\frac{6x^3y^2}{3x^2y^3}\)
2. Simplify: \(\frac{12a^4b^{-3}}{-6a^2b^2}\)
3. Simplify: \(x^2y \times xy^3\)
4. What is \(\frac{8p^5q^{-2}}{4p^3q}\)?
5. Simplify: \(\frac{-9m^4n^3}{3m^2n^5}\)

**Tip:** When dividing powers with the same base, subtract the exponents!

Simplify the expression: \(\frac{-2u^2v^1 \times 8u^3v^{-2}}{4u^1v^2}\).

Learn how to simplify the algebraic expression \(\frac{-2u^2v^1 \times 8u^3v^{-2}}{4u^1v^2}\) step by step using exponent rules. This problem covers key algebraic concepts such as product and division of powers, ideal for students in Grades 8-10.

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