What is e^{-2t}(sin^2(4t)+cos(8t)) ?

The solution to e^{-2t}(sin^2(4t)+cos(8t)) is (sin^2(4t)+cos(8t))/(e^{2t)}

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simplify e^{-2t}(sin^2(4t)+cos(8t))

simplify

e^{- 2 t} (sin^{2} (4 t) + cos (8 t))

\frac{sin ^{2} ( 4 t ) + cos ( 8 t )}{e ^{2 t}}

Solution steps

e^{- 2 t} (sin^{2} (4 t) + cos (8 t))

Apply exponent rule:

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

= \frac{1}{e ^{2 t}} (sin^{2} (4 t) + cos (8 t))

Multiply fractions:

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

= \frac{1 \cdot ( sin ^{2} ( 4 t ) + cos ( 8 t ) )}{e ^{2 t}}

1 \cdot (sin^{2} (4 t) + cos (8 t)) = sin^{2} (4 t) + cos (8 t)

= \frac{sin ^{2} ( 4 t ) + cos ( 8 t )}{e ^{2 t}}

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

(p - 1)^{2} (q - 1)^{2}

e^{- a t} \cdot e^{- s t}

e^{- \frac{5}{4} l n (2)}

10 e^{- \frac{5}{10}}

What is e^{-2t}(sin^2(4t)+cos(8t)) ?
The solution to e^{-2t}(sin^2(4t)+cos(8t)) is (sin^2(4t)+cos(8t))/(e^{2t)}