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Negative base and odd exponent

Theory

Negative base and odd exponent

A power with a negative base and an odd exponent is always negative. Therefore, the parentheses can be omitted. (-8)5=-85 (\text{-} 8)^5=\text{-} 8^5 The odd exponent means that there are an odd number of negative factors in the product, and the product of each pair is positive. (-8)(-8)(-8)Positive(-8)(-8)Positive (\text{-}8)\underbrace{(\text{-}8)(\text{-}8)}_{\text{Positive}}\underbrace{(\text{-}8)(\text{-}8)}_{\text{Positive}} This means that the product of all factors except one is positive. And the product of a positive and negative number is always negative. -884=-85 \text{-} 8\cdot8^4 = \text{-}8^5