![To simplify the expression \( 13(6x^2y)^2(2x^3y^4) \), follow these steps:
1. **Square the first term**:
\[
(6x^2y)^2 = 36x^4y^2
\]
2. **Multiply by the second term**:
\[
36x^4y^2 \cdot (2x^3y^4) = 36 \cdot 2 \cdot x^4 \cdot x^3 \cdot y^2 \cdot y^4 = 72x^{4+3}y^{2+4} = 72x^7y^6
\]
3. **Multiply by 13**:
\[
13 \cdot 72x^7y^6 = 936x^7y^6
\]
Next, check if we can express 936 in terms of the answer choices:
- \( 936 = 24 \cdot 39 \)
- It can also be factored into](https://theinternetioimages-f2htc2ggcrath6d7.z01.azurefd.net/$web/askai/eafa5518-24a9-43e9-b260-7cff39e66ab2.webp)
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Question: Which expression is equivalent to 13(6x2y)2(2x3y4) for all values of x and y where the expression is defined? A.4x12y8 B.4x7y6 C.24x7y6 D.24x12y8
Let's simplify the given expression \(13(6x^2y)^2(2x^3y^4)\). First, simplify \((6x^2y)^2\): \[ (6x^2y)^2 = 6^2 \cdot (x^2)^2 \cdot y^2 = 36x^4y^2 \] Next, multiply this by \(2x^3y^4\): \[ 36x^4y^2 \cdot 2x^3y^4 = 36 \cdot 2 \cdot x^4 \cdot x^3 \cdot y^2 \cdot y^4 = 72x^7y^6 \] Finally, multiply this by 13: \[ 13 \cdot 72x^7y^6 = 936x^7y^6 \] So, the equivalent expression is \(\boxed{936x^7y^6}\). None of the suggested answer choices match this simplified result, which suggests an error in the original choices provided. However, confirming this with our calculation would lead to identifying the most similar/incorrect options: - \(4x^{12}y^8\) - \(4x^7y^6\) - \(24x^7y^6\) - \(24x^{12}y^8\) None match \(936x^7y^6\), so reevaluating if a simpler form and hint links might suggest reviewing similar closely options for different aggregated setups.
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