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Popular >

simplify (e^{x^5+ln(x)})^{-1}

Solution

simplify

(e^{x^{5} + l n (x)})^{- 1}

Solution

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

Solution steps

(e^{x^{5} + l n (x)})^{- 1}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= e^{(x^{5} + l n (x)) (- 1)}

Simplify

(x^{5} + ln (x)) (- 1) : - (x^{5} + ln (x))

= e^{- (x^{5} + l n (x))}

Expand

- (x^{5} + ln (x)) : - x^{5} - ln (x)

= e^{- x^{5} - l n (x)}

Apply exponent rule:

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

= e^{- l n (x)} e^{- x^{5}}

Simplify

e^{- l n (x)} : x^{- 1}

= x^{- 1} e^{- x^{5}}

Simplify

= \frac{e ^{- x^{5}}}{x}

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Frequently Asked Questions (FAQ)

What is (e^{x^5+ln(x)})^{-1} ?
The solution to (e^{x^5+ln(x)})^{-1} is (e^{-x^5})/x