- Explain why a negative number raised to an odd power will always have a negative 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. \(\text{See worked solution}\)
a. \(\text{A negative number multiplied by a negative}\)
\(\text{number an odd number of times always a has}\)
\(\text{negative answer.}\)
\(\text{It therefore, follows that when a negative number}\)
\(\text{is raised to an odd power, such as 1, 3, 5…, }\)
\(\text{the answer is also always negative.}\)
\(\text{ie } (-\times -)\times – =+\times -=-\)
b. \(\text{Examples (Others are also acceptable)}\)
\((-1)^3=(-1\times -1)\times -1=1\times -1=-1\)
\((-1)^5=(-1\times -1)\times (-1\times -1)\times -1=1\times 1\times -1=-1\)