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Popular >

simplify (e^{-(ln(x))/2})^2

Solution

simplify

(e^{- \frac{l n ( x )}{2}})^{2}

Solution

\frac{1}{x}

Solution steps

(e^{- \frac{l n ( x )}{2}})^{2}

Apply exponent rule:

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

= e^{(- \frac{l n ( x )}{2}) \cdot 2}

Simplify

(- \frac{ln ( x )}{2}) \cdot 2 : - ln (x)

= e^{- l n (x)}

Apply exponent rule:

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

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

Apply log rule:

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

e^{l n (x)} = x

= x^{- 1}

Apply exponent rule:

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

= \frac{1}{x}

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Frequently Asked Questions (FAQ)

What is (e^{-(ln(x))/2})^2 ?
The solution to (e^{-(ln(x))/2})^2 is 1/x