What is (e^{x^2})/(e^{ln(x^2))} ?

The solution to (e^{x^2})/(e^{ln(x^2))} is (e^{x^2})/(x^2)

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

simplify

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

\frac{e ^{x^{2}}}{x ^{2}}

Solution steps

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

Apply exponent rule:

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

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

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

assuming

x \geq 0

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

Apply exponent rule:

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

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

Simplify

e^{- 2 l n (x)} : x^{- 2}

= x^{- 2} e^{x^{2}}

Simplify

= \frac{e ^{x^{2}}}{x ^{2}}

e^{2 l n (t) + C} 0

(m^{5} n^{3}) x m^{2} n

\frac{1}{24} (t - 4)^{4} e^{- 3 (t - 4)} u (t - 4)

e^{- (t - \frac{π}{4})}

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