Let's simplify the expression:

$x \sqrt{x^6}$

Step 1: Simplify the square root

Recall that the square root of $x^6$ can be written as:

$\sqrt{x^6} = x^{\frac{6}{2}} = x^3$

Step 2: Multiply the expression

Now, substitute this result back into the original expression:

$x \cdot x^3$

By using the rule of exponents $x^a \cdot x^b = x^{a+b}$, we get:

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

Final Answer:

$x \sqrt{x^6} = x^4$

Would you like further clarification or a breakdown of the steps?

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Related Questions:

1. How do you simplify other radical expressions like $\sqrt{x^8}$?
2. What is the rule for multiplying powers with the same base?
3. Can you simplify expressions involving higher powers or roots?
4. What are the general rules for exponents?
5. How can you solve for $x$ in an equation involving exponents like this?

Tip: Always simplify exponents first before trying to combine terms.