It seems you're asking for the product of the cube root ($\sqrt[3]{x}$) and the fourth root ($\sqrt[4]{x}$) of $x$.

This can be written as:

[ \sqrt[3]{x} \times \sqrt[4]{x} ]

To simplify this expression, recall that $\sqrt[n]{x} = x^{1/n}$. So, we can rewrite the terms as:

$x^{1/3} \times x^{1/4}$

When multiplying powers with the same base, you add the exponents:

$x^{1/3 + 1/4}$

To add the exponents, we need a common denominator. The least common denominator of 3 and 4 is 12. So:

$\frac{1}{3} = \frac{4}{12} \quad \text{and} \quad \frac{1}{4} = \frac{3}{12}$

Now add the exponents:

$\frac{4}{12} + \frac{3}{12} = \frac{7}{12}$

Thus, the product is:

$x^{7/12}$

Final answer:

[ \sqrt[3]{x} \times \sqrt[4]{x} = x^{7/12} ]

Would you like more details on this, or do you have any questions about the steps?

Here are some related questions you might find useful:

1. How do I simplify expressions involving radicals with different roots?
2. What happens when you multiply powers with the same base?
3. How do you add fractions with different denominators?
4. How do fractional exponents work in general?
5. What is the relationship between roots and exponents?

Tip: Always try to rewrite radicals as exponents to simplify expressions; this approach often makes the work much easier.