Answer
$8$
Work Step by Step
THe given expression is equivalent to:
$=2^{\frac{1}{2}}\left(2\cdot 16\right)^{\frac{1}{2}}$
Recall the basic exponent property (pg. 360):
$(ab)^n=a^nb^n$
Applying this property, we get:
$2^{\frac{1}{2}}(2\cdot 16)^{\frac{1}{2}}=2^{\frac{1}{2}}\cdot (2^{\frac{1}{2}}16^{\frac{1}{2}})$
Recall the basic exponent property (pg. 360):
$a^ma^n=a^{m+n}$
Applying this property, we get:
$2^{\frac{1}{2}}\cdot (2^{\frac{1}{2}}16^{\frac{1}{2}})$
$=2^{\frac{1}{2}+\frac{1}{2}}\cdot16^{\frac{1}{2}}$
$=2^{1}\cdot16^{1/2}$
$=2 \cdot16^{1/2}$
Note that $4^2=16$.
Recall that $a^{\frac{1}{2}}=\sqrt{a}$.
Thus, the expression above simplifies to:
$=2\sqrt{16}$
$=2\cdot4$
$=8$
