1. **State the problem:** Simplify the expression $$\frac{3^{25}}{3^{28}}$$ and express it in the form $$3^5 - \text{something}$$.
2. **Recall the exponent division rule:** When dividing powers with the same base, subtract the exponents:
$$\frac{a^m}{a^n} = a^{m-n}$$
3. **Apply the rule:**
$$\frac{3^{25}}{3^{28}} = 3^{25-28}$$
4. **Calculate the exponent:**
$$25 - 28 = -3$$
5. **Rewrite the expression:**
$$\frac{3^{25}}{3^{28}} = 3^{-3}$$
6. **Express in terms of positive exponents:**
$$3^{-3} = \frac{1}{3^3} = \frac{1}{27}$$
7. **Compare with the form $$3^5 - \text{something}$$:**
Since $$3^{-3}$$ is not equal to $$3^5 - \text{something}$$ directly, the expression $$3^5 - \text{something}$$ is not equivalent to $$\frac{3^{25}}{3^{28}}$$.
**Final simplified form:**
$$\frac{3^{25}}{3^{28}} = 3^{-3} = \frac{1}{27}$$
Exponent Division 2Ddbc4
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