Which multiplication expression is equivalent to The simplified quotient is \( \begin{array}{l}\frac{x+8}{x^{2}} \div \frac{2 x+16}{2 x^{2}} ? \\ \\ \frac{x^{2}}{x+8} \cdot \frac{2 x^{2}}{2 x+16} \\ \frac{x+8}{x^{2}} \cdot \frac{2 x+16}{2 x^{2}} \\ \frac{x+8}{x^{2}} \cdot \frac{2 x^{2}}{2 x+16} \\ \text { COMPLETB }\end{array} \)

To solve the expression, let's first simplify the division: \( \frac{x+8}{x^{2}} \div \frac{2x+16}{2x^{2}} \). Dividing by a fraction is the same as multiplying by its reciprocal. So, we can rewrite the division as \( \frac{x+8}{x^{2}} \cdot \frac{2x^{2}}{2x+16} \). This makes it clear that the correct multiplication expression is indeed \( \frac{x+8}{x^{2}} \cdot \frac{2x^{2}}{2x+16} \). Now, keep in mind that \( 2x + 16 \) can be factored out as \( 2(x + 8) \). This means that before we multiply, we can simplify further. Both \( 2x+16 \) and \( x+8 \) share a common factor, which may lead to even more delightful simplifications! Recognizing these common factors can help in problem-solving and understanding the underlying relationships between the expressions.