Pregunta
Simplify: \( \left(4 x^{4} y^{3}\right)\left(4 x^{4}\right) \) A \( 16 x^{16} y^{3} \) (B \( 8 x^{16} y^{3} \) C \( 8 x^{8} y^{3} \) (D) \( 16 x^{8} y^{3} \)
Ask by Watkins Paul. in the United States
Jan 28,2025
Solución de inteligencia artificial de Upstudy
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The simplified expression is \( 16 x^{8} y^{3} \), so the correct answer is (D).
Solución
To simplify the expression \( \left(4 x^{4} y^{3}\right)\left(4 x^{4}\right) \), follow these steps:
1. **Multiply the coefficients (constants):**
\[
4 \times 4 = 16
\]
2. **Multiply the \( x \)-terms:**
\[
x^{4} \times x^{4} = x^{4+4} = x^{8}
\]
3. **Multiply the \( y \)-terms:**
Since there's only one \( y \)-term in the first factor and none in the second, it remains unchanged:
\[
y^{3}
\]
Putting it all together:
\[
\left(4 x^{4} y^{3}\right)\left(4 x^{4}\right) = 16 x^{8} y^{3}
\]
**Answer:**
(D) \( 16 x^{8} y^{3} \)
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First, let's break it down! When you multiply two expressions, you simply multiply their coefficients and add the exponents of like bases. So, in our case: 1. Coefficients: \(4 \times 4 = 16\) 2. For \(x\): \(x^4 \times x^4 = x^{4+4} = x^8\) 3. For \(y\): Since there's only \(y^3\) in the first expression, it remains \(y^3\). Putting it all together, we get \(16 x^8 y^3\). Thus, the correct answer is (D) \(16 x^{8} y^{3}\).
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