Rewrite in simplest rational exponent form square root of x times the fourth root of x. Show each step of your process.

• The square root of $x$ can be expressed as $x^{1/2}$.
• The fourth root of $x$ can be expressed as $x^{1/4}$.

So, we have:

$$\sqrt{x} = x^{1/2} \quad \text{and} \quad \sqrt[4]{x} = x^{1/4}$$

• Now, multiply the two expressions:

$$x^{1/2} \times x^{1/4}$$

• When multiplying like bases, add the exponents:

$$x^{1/2 + 1/4}$$

• The common denominator for $1/2$ and $1/4$ is 4:

$$1/2 = 2/4 \quad \text{and} \quad 1/4 = 1/4$$

• Therefore, the expression simplifies to:

$$x^{3/4}$$

So, the simplest rational exponent form of $\sqrt{x} \times \sqrt[4]{x}$ is $x^{3/4}$.