Compute 7^2 * 7^-5.

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Multiple Choice

Compute 7^2 * 7^-5.

Explanation:
When you multiply powers with the same base, you add the exponents. So 7^2 * 7^-5 becomes 7^(2 + (-5)) = 7^-3. A negative exponent means you take the reciprocal, so 7^-3 = 1/7^3. Since 7^3 = 343, the result is 1/343. That matches the value shown. The other possibilities would come from either ignoring the negative exponent (which would give 343) or incorrectly attaching a negative sign, which doesn’t occur here.

When you multiply powers with the same base, you add the exponents. So 7^2 * 7^-5 becomes 7^(2 + (-5)) = 7^-3. A negative exponent means you take the reciprocal, so 7^-3 = 1/7^3. Since 7^3 = 343, the result is 1/343. That matches the value shown. The other possibilities would come from either ignoring the negative exponent (which would give 343) or incorrectly attaching a negative sign, which doesn’t occur here.

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