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Popular >

simplify (e^x)/((e^x)^x)

Solution

simplify

\frac{e ^{x}}{( e ^{x} ) ^{x}}

Solution

e^{x (- x + 1)}

Solution steps

\frac{e ^{x}}{( e ^{x} ) ^{x}}

Apply exponent rule:

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

\frac{e ^{x}}{( e ^{x} ) ^{x}} = (\frac{e}{e ^{x}})^{x}

= (\frac{e}{e ^{x}})^{x}

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

= (e^{1 - x})^{x}

Apply exponent rule:

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

= e^{(1 - x) x}

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Frequently Asked Questions (FAQ)

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