What is 2xe^{-3x}*e^{3x} ?

The solution to 2xe^{-3x}*e^{3x} is 2x

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simplify 2xe^{-3x}*e^{3x}

simplify

2 x e^{- 3 x} \cdot e^{3 x}

2 x

Solution steps

2 x e^{- 3 x} e^{3 x}

Apply exponent rule:

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

e^{- 3 x} e^{3 x} = e^{- 3 x + 3 x}

= 2 x e^{- 3 x + 3 x}

Add similar elements:

- 3 x + 3 x = 0

= 2 x e^{0}

Apply rule

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

e^{0} = 1

= 2 \cdot 1 \cdot x

Multiply the numbers:

2 \cdot 1 = 2

= 2 x

(x - 2)^{2} \cdot (x - 3)^{2}

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

(a b^{2} c^{- 3})^{- 2 \circ} (a b^{2} c)