Answer
$\sqrt[4]{11^3}$
Work Step by Step
Recall:
$\sqrt[n]{x}=x^{\frac{1}{n}}$
Thus, the given expression above is equivalent to:
$=\sqrt[2]{11}\sqrt[4]{11}$
$=11^{\frac{1}{2}} \cdot 11^{\frac{1}{4}}$
Recall the basic exponent property (pg. 360):
$a^ma^n=a^{m+n}$
Applying this property, the expression above simplifies to:
$=11^{\frac{1}{2}+\frac{1}{4}}$
$=11^{\frac{2}{4}+\frac{1}{4}}$
$=11^{\frac{3}{4}}$
Recall the basic exponent property (pg. 360):
$a^{\frac{m}{n}}=\sqrt[n]{a^m}$
Applying this property, we get:
$11^{\frac{3}{4}}=\sqrt[4]{11^3}$
