Subjects algebra

Simplify Exponents C092F9

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Question: Simplify $\frac{2^{-2}m^{-3}}{n^{0}}$. Write your answer using only positive exponents.
1. **State the problem:** Simplify the expression $$\frac{2^{-2}m^{-3}}{n^{0}}$$ and write the answer using only positive exponents. 2. **Recall important rules:** - Any number raised to the zero power is 1, so $$n^{0} = 1$$. - Negative exponents mean the reciprocal, for example, $$a^{-b} = \frac{1}{a^{b}}$$. 3. **Simplify the denominator:** Since $$n^{0} = 1$$, the expression becomes: $$\frac{2^{-2}m^{-3}}{1} = 2^{-2}m^{-3}$$ 4. **Rewrite negative exponents as positive:** $$2^{-2} = \frac{1}{2^{2}} = \frac{1}{4}$$ $$m^{-3} = \frac{1}{m^{3}}$$ 5. **Combine the terms:** $$2^{-2}m^{-3} = \frac{1}{4} \times \frac{1}{m^{3}} = \frac{1}{4m^{3}}$$ **Final answer:** $$\boxed{\frac{1}{4m^{3}}}$$