Evaluate (-4)^-3

Problem

(−4)(−3)

Solution

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

2. Apply the rule to rewrite the expression as a fraction with a positive exponent in the denominator.

(−4)(−3)=1/((−4)3)

3. Calculate the power in the denominator by multiplying the base by itself three times.

(−4)3=(−4)⋅(−4)⋅(−4)

4. Simplify the product, noting that a negative number raised to an odd power results in a negative value.

(−4)⋅(−4)=16

16⋅(−4)=−64

5. Substitute the result back into the fraction.

1/(−64)=−1/64

Final Answer

(−4)(−3)=−1/64

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