The equation you provided is:

$(2x^{\frac{1}{2}}) - (x^{\frac{1}{4}}) = 0$

Let's solve it step by step:

Step 1: Isolate the terms

Move one of the terms to the other side of the equation:

$2x^{\frac{1}{2}} = x^{\frac{1}{4}}$

Step 2: Express the exponents as powers

We can rewrite this in a more manageable form by expressing both sides as powers of $x$:

$2(x^{\frac{1}{2}}) = x^{\frac{1}{4}}$

Step 3: Divide both sides by $x^{\frac{1}{4}}$

Divide both sides by $x^{\frac{1}{4}}$ to simplify the equation:

$2x^{\frac{1}{2} - \frac{1}{4}} = 1$

Simplify the exponent:

$2x^{\frac{1}{4}} = 1$

Step 4: Solve for $x^{\frac{1}{4}}$

Now, divide both sides by 2:

$x^{\frac{1}{4}} = \frac{1}{2}$

Step 5: Raise both sides to the power of 4

To get $x$ by itself, raise both sides to the power of 4:

$x = \left( \frac{1}{2} \right)^4$

$x = \frac{1}{16}$

Final Answer:

$x = \frac{1}{16}$

If you have any questions or want further details, feel free to ask!

Here are 5 related questions for practice:

1. Solve $(3x^{\frac{1}{2}}) - (x^{\frac{1}{4}}) = 0$.
2. Solve $4x^{\frac{1}{3}} = 16x^{\frac{1}{6}}$.
3. If $y = x^{\frac{1}{2}}$, solve for $x$ when $y = 5$.
4. Solve $x^{\frac{1}{3}} - x^{\frac{1}{6}} = 0$.
5. Simplify and solve $x^{\frac{2}{3}} = 9$.

Tip: When dealing with fractional exponents, remember that $x^{m/n}$ is the same as $\sqrt[n]{x^m}$, which helps in solving powers and roots.