What is 2e^{-2t} 1/(sqrt(2)) ?

The solution to 2e^{-2t} 1/(sqrt(2)) is (sqrt(2))/(e^{2t)}

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simplify 2e^{-2t} 1/(sqrt(2))

simplify

2 e^{- 2 t} \frac{1}{2}

\frac{2}{e ^{2 t}}

Solution steps

2 e^{- 2 t} \frac{1}{2}

Apply exponent rule:

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

= 2 \cdot \frac{1}{2} \cdot \frac{1}{e ^{2 t}}

Multiply fractions:

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

= \frac{1 \cdot 1 \cdot 2}{e ^{2 t} 2}

Multiply the numbers:

1 \cdot 1 \cdot 2 = 2

= \frac{2}{2 e ^{2 t}}

Apply radical rule:

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

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

Apply exponent rule:

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

\frac{2 ^{1}}{2 ^{\frac{1}{2}}} = 2^{1 - \frac{1}{2}}

= \frac{2 ^{1 - \frac{1}{2}}}{e ^{2 t}}

Subtract the numbers:

1 - \frac{1}{2} = \frac{1}{2}

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

Apply radical rule:

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

= \frac{2}{e ^{2 t}}

(8.7 \cdot 1 0^{7}) (1.9 \cdot 1 0^{11})

\frac{( 1 + cot ( x ) ) ^{2}}{( 1 - cot ( x ) ) ^{2}}

1 e^{- s t}

What is 2e^{-2t} 1/(sqrt(2)) ?
The solution to 2e^{-2t} 1/(sqrt(2)) is (sqrt(2))/(e^{2t)}