Question

Help!? i dont understand. First question on top, and second question in bottom

Answer 1

We know that:

$\sqrt[a]{x^b}=x^{\frac{b}{a}}$

so:

1)

$(\sqrt[3]{t^4})\cdot(t^{\frac{-1}{2}})=(t^{\frac{4}{3}})\cdot(t^{\frac{-1}{2}})= t^{\frac{4}{3}+\frac{-1}{2}}=t^{\frac{8}{6}+\frac{-3}{6}}=t^{\frac{8-3}{6}}=\boxed{t^{\frac{5}{6}}=\sqrt[6]{t^5}}$

2)

$x^{-\frac{2}{5}}=\dfrac{1}{x^{\frac{2}{5}}}=\boxed{\dfrac{1}{\sqrt[5]{x^2}}}$

Answer 4)