Answer
$\dfrac{1}{20}$
Work Step by Step
To find the root of this radical, we will rewrite the radicand as a base raised to the 4th power because we want to take the 4th root of this number. Because the radicand is a fraction, we rewrite the numerator as a base raised to the 4th power ($1^4$) and the denominator as a base raised to the 4th power ($20^4$):
$\sqrt[4] {\dfrac{1}{160,000}}$ = $\sqrt[4] {\dfrac{1^{4}}{20^{4}}}$
To get rid of the radical, we take the 4th root of $1^4$ in the numerator and $20^4$ in the denominator:
$\sqrt[4] {160,000}$ = $\dfrac{1}{20}$
We only want to take the real roots, so $\frac{1}{20}$ is a valid answer because all rational numbers are real numbers.
