Evaluate (-5)^-3

Problem

(−5)(−3)

Solution

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

1/((−5)3)

2. Expand the power in the denominator by multiplying the base by itself three times.

1/((−5)⋅(−5)⋅(−5))

3. Calculate the product of the negative numbers, noting that an odd number of negative factors results in a negative product.

(−5)⋅(−5)=25

25⋅(−5)=−125

4. Simplify the fraction by placing the negative sign in front of the fraction or in the numerator.

−1/125

Final Answer

(−5)(−3)=−1/125

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