Answer
$3\sqrt[3]{3}$
Work Step by Step
Recall the rational exponent property (pg. 382):
$\sqrt[n]{a}=a^{\frac{1}{n}}$
Applying this property, the given expression is equivalen to:
$=9^{\frac{1}{3}}9^{\frac{1}{3}}$
Next, recall the basic exponent property (pg. 360):
$(ab)^n=a^nb^n$
Applying this property to our last expression above, we get:
$=(9\cdot9)^{\frac{1}{3}}$
$=(81)^{\frac{1}{3}}$
$=(27\cdot3)^{\frac{1}{3}}$
Splitting again into two exponents, we get:
$=(27)^{\frac{1}{3}}(3)^{\frac{1}{3}}$
Using the previously given exponent property, we rewrite the result as a radical:
$=\sqrt[3]{27}\cdot\sqrt[3]{3}$
Since $3^3=27$, then the expression above simplifies to:
$=3\sqrt[3]{3}$
