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

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

UpStudy AI · Accepted Answer

We start with the original quotient:

$$
\frac{x+8}{x^2} \div \frac{2x+16}{2x^2}
$$

Recall that dividing by a fraction is equivalent to multiplying by its reciprocal. That is,

$$
a \div b = a \cdot \frac{1}{b}
$$

Thus, the quotient is equivalent to:

$$
\frac{x+8}{x^2} \cdot \left(\frac{2x+16}{2x^2}\right)^{-1} = \frac{x+8}{x^2} \cdot \frac{2x^2}{2x+16}
$$

So the expression:

$$
\frac{x+8}{x^2} \cdot \frac{2x^2}{2x+16}
$$

is equivalent to the simplified quotient, which corresponds to the third multiplication expression provided.

Thus, the correct multiplication expression is:

$$
\frac{x+8}{x^{2}} \cdot \frac{2 x^{2}}{2 x+16}
$$
The equivalent multiplication expression is $$ \frac{x+8}{x^{2}} \cdot \frac{2 x^{2}}{2 x+16} $$.

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