radical equation

Problem 7
Determine the value of $x$ from $\sqrt[4]{3^{x^2}\sqrt{3^{x - 1}}} = \sqrt[8]{9^{x + 1}}$
 

Problem
Solve for x and y from the given system of equations.
$x + 2y = 6$   ←   Equation (1)

$\sqrt{x} + \sqrt{y} = 3$   ←   Equation (2)
 

Solve for $x$ from the following equations:

5. $\left( \dfrac{x^2 - 15}{x} \right)^2 - 16\left( \dfrac{15 - x^2}{x} \right) + 28 = 0$
    
6. $\dfrac{x}{\sqrt{x} + \sqrt{9 - x}} + \dfrac{x}{\sqrt{x} - \sqrt{9 - x}} = \dfrac{24}{\sqrt{x}}$

Determine the value of $x$ from the following equations:

3. $\sqrt{(4 - x^2)^3} + 3x^2\sqrt{4 - x^2} = 0$
    
4. $\dfrac{1}{3x - 2} - \dfrac{8}{\sqrt{3x - 2}} = 9$
    

Solve for $x$ from the following equations

1. $\sqrt{3 - x} + \sqrt{4 - 2x} = \sqrt{3 - 3x}$
    
2. $\sqrt{\dfrac{2x + 4}{x - 5}} + 8\sqrt{\dfrac{x - 5}{2x + 4}} = 6$