What is simplify-e^{-k}*(-e^{-k}) ?

The solution to simplify-e^{-k}*(-e^{-k}) is 1/(e^{2k)}

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simplify-e^{-k}*(-e^{-k})

simplify

- e^{- k} \cdot (- e^{- k})

\frac{1}{e ^{2 k}}

Solution steps

- e^{- k} (- e^{- k})

Apply exponent rule:

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

= - \frac{1}{e ^{k}} (- e^{- k})

Apply rule

- (- a) = a

= \frac{1}{e ^{k}} e^{- k}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot e ^{- k}}{e ^{k}}

Multiply:

1 \cdot e^{- k} = e^{- k}

= \frac{e ^{- k}}{e ^{k}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{e ^{- k}}{e ^{k}} = e^{- k - k} = e^{- 2 k}

= \frac{1}{e ^{2 k}}

(3 a^{2}) (4 a^{2})

e^{- 11000 \cdot 8}

(4 x y) (2 x^{2} y^{3})

4.1 x 1 0^{- 7}

(4 y) (2 y^{2})

What is simplify-e^{-k}*(-e^{-k}) ?
The solution to simplify-e^{-k}*(-e^{-k}) is 1/(e^{2k)}