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Popular >

simplify x^{-3}e^y(e^{-y})

Solution

simplify

x^{- 3} e^{y} (e^{- y})

Solution

\frac{1}{x ^{3}}

Solution steps

x^{- 3} e^{y} (e^{- y})

Apply exponent rule:

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

e^{y} e^{- y} = e^{y - y}

= x^{- 3} e^{y - y}

Add similar elements:

y - y = 0

= x^{- 3} e^{0}

Apply rule

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

e^{0} = 1

= 1 \cdot x^{- 3}

Apply exponent rule:

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

x^{- 3} = \frac{1}{x ^{3}}

= 1 \cdot \frac{1}{x ^{3}}

Multiply:

\frac{1}{x ^{3}} \cdot 1 = \frac{1}{x ^{3}}

= \frac{1}{x ^{3}}

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Frequently Asked Questions (FAQ)

What is x^{-3}e^y(e^{-y}) ?
The solution to x^{-3}e^y(e^{-y}) is 1/(x^3)