Subjects algebra

Exponent Division 2Ddbc4

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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:** $$\frac{3^{25}}{3^{28}} = 3^{-3} = \frac{1}{27}$$