Evaluate (-9)^-2

Problem

(−9)^(−2)

Solution

1. Apply the negative exponent rule, which states that a^(−n)=1/(a^n) for any non-zero base a

1/((−9)^2)

2. Evaluate the power in the denominator by multiplying the base by itself.

(−9)^2=(−9)⋅(−9)

3. Simplify the product noting that a negative number multiplied by a negative number results in a positive number.

(−9)⋅(−9)=81

4. Substitute the value back into the fraction.

1/81

Final Answer

(−9)^(−2)=1/81

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