Evaluate (-2)^-4

Problem

(−2)(−4)

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.

(−2)(−4)=1/((−2)4)

3. Evaluate the power in the denominator by multiplying the base −2 by itself 4 times.

(−2)4=(−2)⋅(−2)⋅(−2)⋅(−2)

4. Calculate the product, noting that a negative number raised to an even power results in a positive value.

(−2)4=16

5. Substitute the value back into the fraction.

1/16

Final Answer

(−2)(−4)=1/16

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