What is 4(1-(1-e^{6-y}))^{4-1}e^{-(y-6)} ?

The solution to 4(1-(1-e^{6-y}))^{4-1}e^{-(y-6)} is 4e^{-4y+24}

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simplify 4(1-(1-e^{6-y}))^{4-1}e^{-(y-6)}

simplify

4 (1 - (1 - e^{6 - y}))^{4 - 1} e^{- (y - 6)}

4 e^{- 4 y + 24}

Solution steps

4 (1 - (1 - e^{6 - y}))^{4 - 1} e^{- (y - 6)}

Apply exponent rule:

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

= 4 \cdot \frac{1}{e ^{(y - 6)}} (- (- e^{- y + 6} + 1) + 1)^{4 - 1}

Remove parentheses:

(a) = a

= 4 (1 - (1 - e^{6 - y}))^{4 - 1} \frac{1}{e ^{y - 6}}

(1 - (1 - e^{6 - y}))^{4 - 1} = e^{3 (- y + 6)}

= 4 e^{3 (- y + 6)} \frac{1}{e ^{y - 6}}

Multiply fractions:

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

= \frac{1 \cdot 4 e ^{(- y + 6) \cdot 3}}{e ^{y - 6}}

Multiply the numbers:

1 \cdot 4 = 4

= \frac{4 e ^{3 (- y + 6)}}{e ^{y - 6}}

Apply exponent rule:

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

\frac{e ^{3 (- y + 6)}}{e ^{y - 6}} = e^{3 (- y + 6) - (y - 6)} = e^{- 4 y + 24}

= 4 e^{- 4 y + 24}

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1 0^{6} \cdot 12 \cdot 1 0^{(- 3)} \frac{1}{π \cdot 357}

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What is 4(1-(1-e^{6-y}))^{4-1}e^{-(y-6)} ?
The solution to 4(1-(1-e^{6-y}))^{4-1}e^{-(y-6)} is 4e^{-4y+24}