Subjects algebra

Negative Exponent 970A4E

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1. **State the problem:** Simplify the expression $7^{-2}$ and express it as a fraction. 2. **Recall the negative exponent rule:** For any nonzero number $a$ and integer $n$, $a^{-n} = \frac{1}{a^n}$. 3. **Apply the rule:** $$7^{-2} = \frac{1}{7^2}$$ 4. **Calculate the denominator:** $$7^2 = 7 \times 7 = 49$$ 5. **Write the final simplified form:** $$7^{-2} = \frac{1}{49}$$ **Explanation of the boxes:** - Box 1A contains the base $7$. - Box 1B contains the exponent $2$. - Box 1C contains the calculated value $49$. Thus, the expression $7^{-2} = \frac{1}{7 \times 7} = \frac{1}{49}$.