What is e^{-2x}\times 2e^{2x} ?

The solution to e^{-2x}\times 2e^{2x} is 2

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simplify e^{-2x}\times 2e^{2x}

simplify

e^{- 2 x} \cdot 2 e^{2 x}

2

Solution steps

e^{- 2 x} \cdot 2 e^{2 x}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

e^{- 2 x} e^{2 x} = e^{- 2 x + 2 x}

= 2 e^{- 2 x + 2 x}

Add similar elements:

- 2 x + 2 x = 0

= 2 e^{0}

Apply rule

a^{0} = 1, a \neq = 0

e^{0} = 1

= 2 \cdot 1

Multiply the numbers:

2 \cdot 1 = 2

= 2

y^{2} (x^{5} y^{3})

- 2000 \cdot e^{- \frac{π}{2}}

x^{3} \times y^{3}

- a e^{- x}

- e^{- \frac{0}{3}}