What is simplify-16e^{2t}sin(2t)*e^{-2t}(2sin(2t)) ?

The solution to simplify-16e^{2t}sin(2t)*e^{-2t}(2sin(2t)) is -32sin^2(2t)

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simplify-16e^{2t}sin(2t)*e^{-2t}(2sin(2t))

simplify

- 16 e^{2 t} sin (2 t) \cdot e^{- 2 t} (2 sin (2 t))

- 32 sin^{2} (2 t)

Solution steps

- 16 e^{2 t} sin (2 t) e^{- 2 t} (2 sin (2 t))

Apply exponent rule:

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

sin (2 t) sin (2 t) = sin^{1 + 1} (2 t)

= - 16 e^{2 t} e^{- 2 t} \cdot 2 sin^{1 + 1} (2 t)

Add the numbers:

1 + 1 = 2

= - 16 e^{2 t} e^{- 2 t} \cdot 2 sin^{2} (2 t)

Apply exponent rule:

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

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

= - 16 e^{2 t - 2 t} \cdot 2 sin^{2} (2 t)

Add similar elements:

2 t - 2 t = 0

= - 16 e^{0} \cdot 2 sin^{2} (2 t)

Apply rule

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

e^{0} = 1

= - 16 \cdot 1 \cdot 2 sin^{2} (2 t)

Multiply the numbers:

16 \cdot 1 \cdot 2 = 32

= - 32 sin^{2} (2 t)

e^{- 1. 5^{0.2}}

1.04 \cdot 1 0^{- 10}

1.284206429 \cdot 1 0^{- 4}

15 e^{- 0.15 (5)}

(6.674 \cdot 1 0^{- 11}) (5.972 \cdot 1 0^{24})

What is simplify-16e^{2t}sin(2t)*e^{-2t}(2sin(2t)) ?
The solution to simplify-16e^{2t}sin(2t)*e^{-2t}(2sin(2t)) is -32sin^2(2t)