onential form where necessary (3) $$ \frac{5^{15}}{5^{12} \cdot 5^{6}} $$

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To simplify the expression $$ \frac{5^{15}}{5^{12} \cdot 5^{6}} $$ using the properties of exponents, follow these steps:

1. **Combine the exponents in the denominator:**
   
   When multiplying powers with the same base, you add the exponents:
   $$
   5^{12} \cdot 5^{6} = 5^{12 + 6} = 5^{18}
   $$
   
2. **Simplify the fraction:**
   
   Now, the expression becomes:
   $$
   \frac{5^{15}}{5^{18}}
   $$
   
   When dividing powers with the same base, you subtract the exponents:
   $$
   \frac{5^{15}}{5^{18}} = 5^{15 - 18} = 5^{-3}
   $$
   
3. **Express with a positive exponent:**
   
   A negative exponent indicates the reciprocal:
   $$
   5^{-3} = \frac{1}{5^{3}}
   $$
   
4. **Calculate the final value:**
   
   $$
   \frac{1}{5^{3}} = \frac{1}{125}
   $$

**Final Simplified Form:**
$$
\frac{5^{15}}{5^{12} \cdot 5^{6}} = \frac{1}{125}
$$
$$ \frac{5^{15}}{5^{12} \cdot 5^{6}} = \frac{1}{125} $$

onential form where necessary (3) \( \frac{5^{15}}{5^{12} \cdot 5^{6}} \)

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