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Let's analyze the problem given in Question 4:

It asks for the simplified form of:

\[
\sqrt[7]{x} \cdot \sqrt[7]{x} \cdot \sqrt[7]{x}
\]

### Step 1: Use exponent rules
Recall that a radical can be rewritten as an exponent. Specifically:
\[
\sqrt[7]{x} = x^{\frac{1}{7}}
\]

Thus, the given expression becomes:
\[
x^{\frac{1}{7}} \cdot x^{\frac{1}{7}} \cdot x^{\frac{1}{7}}
\]

### Step 2: Apply exponent addition
When multiplying terms with the same base, you add the exponents. So, adding the exponents:
\[
x^{\frac{1}{7}} + x^{\frac{1}{7}} + x^{\frac{1}{7}} = x^{\frac{3}{7}}
\]

### Final Answer:
The simplified form is \( x^{\frac{3}{7}} \), which matches the choice **\(\frac{3}{7}\)** in the options.

Would you like more details on this, or do you have any other questions?

Here are 5 related questions for further practice:
1. What is the simplified form of \( \sqrt[5]{x} \cdot \sqrt[5]{x} \cdot \sqrt[5]{x} \)?
2. How would you simplify \( \sqrt[4]{x^2} \)?
3. Can you explain the exponent rule when dividing terms with the same base?
4. How do you simplify expressions involving both radicals and exponents, like \( x^{\frac{1}{3}} \cdot x^{\frac{1}{6}} \)?
5. What is the general form of a radical in terms of exponents?

**Tip:** Always remember that multiplication of terms with the same base involves adding their exponents.

Which of the following is the simplified form of (7th root of x) * (7th root of x) * (7th root of x)?

Learn how to simplify an expression involving the 7th root of x multiplied by itself three times. Understand the rules of exponents and radicals to solve this problem, suitable for students in Grades 9-11.

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