How to simplify a fraction in a radical

Question

how would you simplify a radical that has the fraction 8 divided by 27 aka 8/27. Step by step.

Answer 1

For $$\sqrt[n]{\dfrac{8}{27}}$$ We can write $\dfrac{8}{27}=\left(\dfrac{2}{3}\right)^3$, so $$\sqrt[n]{\dfrac{8}{27}}=\left(\left(\dfrac{2}{3}\right)^3\right)^{1/n}=\boxed{\left(\dfrac{2}{3}\right)^{\dfrac{3}{n}}}$$