Answer
$7\sqrt{3}$
Work Step by Step
With $21=3\cdot7$, the given expression is equivalent to:
$=7^{\frac{1}{2}}\left(3\cdot7\right)^{\frac{1}{2}}$
Recall the basic exponent property (pg. 360):
$(ab)^n=a^nb^n$
Applying this property, we get:
$=7^{\frac{1}{2}}\cdot 3^{\frac{1}{2}}\cdot 7^{\frac{1}{2}}$
$=7^{\frac{1}{2}}\cdot 7^{\frac{1}{2}}\cdot 3^{\frac{1}{2}}$
Recall the basic exponent property (pg. 360):
$a^ma^n=a^{m+n}$
Applying this property, we get:
$7^{\frac{1}{2}}\cdot 7^{\frac{1}{2}}\cdot 3^{\frac{1}{2}}
\\=7^{\frac{1}{2}+\frac{1}{2}} \cdot 3^{\frac{1}{2}}$
$=7^{1} \cdot 3^{\frac{1}{2}}$
$=7\cdot 3^{\frac{1}{2}}$
$=7\sqrt{3}$
