5. Simplify: $$ \frac{a^{2} imes c^{3}}{a^{3} imes c^{2}} \frac{c^{3} imes a^{2}}{a^{4} imes c^{2} x d x e} $$

Question

5. Simplify: $$ \frac{a^{2} 	imes c^{3}}{a^{3} 	imes c^{2}} \frac{c^{3} 	imes a^{2}}{a^{4} 	imes c^{2} x d x e} $$

UpStudy AI · Accepted Answer

To simplify the expression:

$$
\frac{a^{2} \times c^{3}}{a^{3} \times c^{2}} \times \frac{c^{3} \times a^{2}}{a^{4} \times c^{2} \times d \times e}
$$

**Step 1: Simplify Each Fraction Separately**

1. **First Fraction:**

$$
\frac{a^{2} \times c^{3}}{a^{3} \times c^{2}} = \frac{a^{2}}{a^{3}} \times \frac{c^{3}}{c^{2}} = a^{-1} \times c^{1} = \frac{c}{a}
$$

2. **Second Fraction:**

$$
\frac{c^{3} \times a^{2}}{a^{4} \times c^{2} \times d \times e} = \frac{c^{3}}{c^{2}} \times \frac{a^{2}}{a^{4}} \times \frac{1}{d \times e} = c^{1} \times a^{-2} \times \frac{1}{d \times e} = \frac{c}{a^{2} \times d \times e}
$$

**Step 2: Multiply the Simplified Fractions**

$$
\frac{c}{a} \times \frac{c}{a^{2} \times d \times e} = \frac{c \times c}{a \times a^{2} \times d \times e} = \frac{c^{2}}{a^{3} \times d \times e}
$$

**Final Simplified Expression:**

$$
\frac{c^{2}}{a^{3} \times d \times e}
$$

**Answer:**

\boxed{\dfrac{c^{2}}{a^{3}\, d\, e}}
$$ \frac{c^{2}}{a^{3} \times d \times e} $$

Simplify:

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