Hallo Jerem,
Willkommen in der Mathelounge!
$$x^{\frac{5}{2}}=2 \space \Rightarrow x=2^{\frac{2}{5}}=\sqrt[5]{2^2} \approx 1,320$$
$$x^{\frac{3}{4}}=0,001 \space \Rightarrow x = 0,001^{\frac{4}{3}}={\left(10^{-3}\right)}^{\frac{4}{3}}=10^{(-3 \cdot \frac{4}{3})}=10^{-4}=0,0001$$
$${\sqrt{x}}^3=2 \space \Rightarrow x^{\frac{3}{2}}=2 \space\Rightarrow x=2^{\frac{2}{3}}=\sqrt[3]{2^2} \approx 1,587$$
$${\sqrt[5]{x}}^2=2 \space\Rightarrow x^{\frac{2}{5}}=2 \space\Rightarrow x=2^{\frac{2}{5}}=\sqrt[5]{2^2} \approx 1,320$$
$${\sqrt[6]{x}}^5 = 10^5 \space\Rightarrow x^{\frac{5}{6}}=10^5 \space\Rightarrow x=10^{5 \cdot \frac{6}{5}}=10^6$$
$$x^{0,75}=0,75^{\frac{3}{4}} \space\Rightarrow {\left(0,75^{\frac{3}{4}} \right)}^{\frac{4}{3}}=0,75^{\frac{3}{4} \cdot \frac{4}{3}}=0,75^1=0,75$$
Gruß Werner
