Answer
$3^{\sqrt 2}$
Work Step by Step
Rewrite $9$ as $3^2$:
$\left(3^{2}\right)^\frac{1}{\sqrt 2}$
Simplify the exponent:
$3^{2\cdot\frac{1}{\sqrt2}}=3^{\frac{2}{\sqrt 2}}$
Do not leave radicals in the denominator of any fraction.
To get rid of the radical, multiply both numerator and denominator by the same radical:
$3^{(\frac{2}{\sqrt 2} \cdot \frac{\sqrt 2}{\sqrt 2})}$
Multiply the fractions in the exponent:
$3^{\frac{2\sqrt 2}{\sqrt 4}}$
Simplify the radicals in the exponent:
$3^{\frac{2\sqrt 2}{2}}$
Simplify the fraction in the exponent:
$3^{\sqrt 2}$
