1.19) $$ \frac{5^{3} \cdot 3^{2}}{5^{4} 3}= $$

Question

UpStudy AI · Accepted Answer

To simplify the expression:

$$
\frac{5^{3} \cdot 3^{2}}{5^{4} \cdot 3}
$$

**Step 1: Apply the Quotient Rule for Exponents**

The quotient rule states that $$\frac{a^m}{a^n} = a^{m-n}$$.

Apply this to both the base 5 and base 3 terms separately:

$$
\frac{5^{3}}{5^{4}} = 5^{3-4} = 5^{-1}
$$
$$
\frac{3^{2}}{3} = \frac{3^{2}}{3^{1}} = 3^{2-1} = 3^{1}
$$

**Step 2: Simplify the Expression**

Now, substitute the simplified terms back into the expression:

$$
5^{-1} \cdot 3^{1} = \frac{1}{5} \cdot 3 = \frac{3}{5}
$$

**Final Answer:**

$$
\frac{3}{5}
$$
$$ \frac{3}{5} $$

1.19) \( \frac{5^{3} \cdot 3^{2}}{5^{4} 3}= \)