1. $$x^{\frac{2}{3}}$$
2. $$x^{\frac{7}{3}}$$
3. $$x^{\frac{9}{5}}$$

1. $(x+2)^2 = 9$ also $(x+2)=\pm 3$, also $x_{1}=-5$, $x_=1$.
2. $(x-3)^2 = 4$ also $(x-3)=\pm 2$, also $x_1=1$, $x_2=5$.
3. $(x+4)^2 = 1$ also $(x+4)=\pm 1$, also $x_1=-5$, $x_2=3$.

1.

$\begin{align*} {{15x}\over{8}}+{{4}\over{3}} &= {{7x}\over{4}}+{{13}\over{8}} && |\cdot 24\\ 45x+32 &= 42x+39 && |-\left(42x+32\right)\\ 3x &= 7 && |:3\\ x &= {{7}\over{3}} \end{align*}$

2.

$\begin{align*} {{19x}\over{20}}+{{6}\over{5}} &= {{4x}\over{5}}+{{7}\over{5}} && |\cdot 20\\ 19x+24 &= 16x+28 && |-\left(16x+24\right)\\ 3x &= 4 && |:3\\ x &= {{4}\over{3}} \end{align*}$

3.

$\begin{align*} {{53x}\over{18}}+{{7}\over{6}} &= {{8x}\over{3}}+{{4}\over{3}} && |\cdot 18\\ 53x+21 &= 48x+24 && |-\left(48x+21\right)\\ 5x &= 3 && |:5\\ x &= {{3}\over{5}} \end{align*}$