What is 80te^{-500t}(15te^{-500t}) ?

The solution to 80te^{-500t}(15te^{-500t}) is 1200e^{-1000t}t^2

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simplify 80te^{-500t}(15te^{-500t})

simplify

80 t e^{- 500 t} (15 t e^{- 500 t})

1200 e^{- 1000 t} t^{2}

Solution steps

80 t e^{- 500 t} (15 t e^{- 500 t})

Apply exponent rule:

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

e^{- 500 t} e^{- 500 t} = e^{- 500 t - 500 t}

= 80 t \cdot 15 t e^{- 500 t - 500 t}

Add similar elements:

- 500 t - 500 t = - 1000 t

= 80 t \cdot 15 t e^{- 1000 t}

Apply exponent rule:

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

tt = t^{1 + 1}

= 80 \cdot 15 t^{1 + 1} e^{- 1000 t}

Add the numbers:

1 + 1 = 2

= 80 \cdot 15 t^{2} e^{- 1000 t}

Multiply the numbers:

80 \cdot 15 = 1200

= 1200 e^{- 1000 t} t^{2}

9 - x^{2} \cdot 1 + x

e^{- a s} f (s)

0.00475 \cdot 1 0^{- 3}

(x^{3} y^{6} z) (5 x^{2} y^{12} z)

\frac{( a + b ) ^{4}}{( a - b ) ^{4}}

What is 80te^{-500t}(15te^{-500t}) ?
The solution to 80te^{-500t}(15te^{-500t}) is 1200e^{-1000t}t^2