Subjects algebra

Negative Exponent F34E8E

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1. **State the problem:** Evaluate the expression $$\left( \frac{1}{4} \right)^{-3}$$. 2. **Recall the property of negative exponents:** For any nonzero number $a$ and integer $n$, $$a^{-n} = \frac{1}{a^n}$$. 3. **Apply the property:** $$\left( \frac{1}{4} \right)^{-3} = \left( \frac{1}{4} \right)^{-3} = \left( 4 \right)^3$$ 4. **Calculate the power:** $$4^3 = 4 \times 4 \times 4 = 64$$ 5. **Final answer:** $$\left( \frac{1}{4} \right)^{-3} = 64$$ This means raising a fraction to a negative exponent flips the fraction and raises it to the positive exponent.