Indices, SM-Bank 038

Explain why a negative number raised to an even power will always have a positive answer. (2 marks)

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Give 2 worked examples that verify your explanation. (2 marks)

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a. \(\text{See worked solution}\)

b. \(\text{See worked solution}\)

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a. \(\text{A negative number multiplied by a negative}\)

\(\text{number always a has positive answer.}\)

\(\text{It therefore, follows that when a negative number}\)

\(\text{is multiplied by a negative number, an even}\)

\(\text{number of times, as is the case with even powers}\)

\(\text{such as 2, 4, 6…, the answer is also always positive.}\)

b. \(\text{Examples (Others are also acceptable)}\)

\((-1)^2=-1\times -1=1\)

\((-1)^4=-1\times -1\times -1\times -1=1\)