Answer
$(7x)^{\frac{3}{2}}$
Work Step by Step
We are asked to replace radicals with exponents in the given equation:
$\sqrt[2]{(7x)^3}$
Recall the rational exponent property (pg. 382):
$a^{\frac{m}{n}}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$
Applying this property ($m=3$, $n=2$, $a=7x^3$), we get:
$\sqrt{(7x)^3}=\left[(7x)^3\right]^{\frac{1}{2}}=\left(7x\right)^{\frac{3}{2}}$
