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Popular >

simplify e^{(ln(x))/x}

Solution

simplify

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

Solution

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

Solution steps

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

Simplify

= 1 \cdot ln (x) \frac{1}{x}

= e^{1 \cdot l n (x) \frac{1}{x}}

Apply exponent rule:

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

= (e^{l n (x)})^{1 \cdot \frac{1}{x}}

Apply log rule:

a^{l o g_{a} (b)} = b

e^{l n (x)} = x

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

Multiply:

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

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

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Frequently Asked Questions (FAQ)

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