Explain this answer for differentiating an exponent

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Here is the question and answer - eX What confuses me is how $$\frac{2t}{2e^{2t}}=te^{-2t}$$ What I get is $$\frac{t}{e^{2t}}$$

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Simple exponential properties, by definition

$$a^{-b} = \frac{1}{a^b}$$