To simplify the expression \(\frac{(x^2)^3 \times x}{x^7}\), let's follow these steps:

1. **Simplify the exponent:**  
   \((x^2)^3 = x^{2 \times 3} = x^6\).

   Now the expression becomes:
   \[
   \frac{x^6 \times x}{x^7}
   \]

2. **Combine the terms in the numerator:**  
   Using the rule \(x^a \times x^b = x^{a+b}\), we get:
   \[
   x^6 \times x = x^{6+1} = x^7
   \]

   Now the expression is:
   \[
   \frac{x^7}{x^7}
   \]

3. **Simplify the fraction:**  
   Using the rule \(\frac{x^a}{x^b} = x^{a-b}\), we have:
   \[
   \frac{x^7}{x^7} = x^{7-7} = x^0
   \]

4. **Simplify \(x^0\):**  
   \(x^0 = 1\), for any \(x \neq 0\).

So, the simplified expression is:
\[
\boxed{1}
\]

Would you like more details or have any questions?

Here are some related questions for further practice:

1. Simplify \(\frac{(y^3)^2 \times y^4}{y^9}\).
2. What is \(\frac{(2x^2)^3 \times 4x}{8x^7}\)?
3. Simplify \(x^{10} \times x^{-3}\).
4. Simplify \(\frac{x^{a+b} \times x^{c}}{x^{d}}\).
5. What is \(\frac{y^5 \times y^2}{y^3}\)?
6. Simplify \(\frac{(3x^2)^2 \times 9x}{x^8}\).
7. What is the value of \(\frac{a^3 \times a}{a^4}\)?
8. Simplify \(\frac{(x^4)^2 \times x}{x^9}\).

**Tip:** Remember that any non-zero number raised to the power of zero is always equal to 1.

Learn how to simplify the expression (x^2)^3 * x / x^7 step-by-step with clear explanations and examples. This problem covers key algebraic concepts including exponents and simplifying expressions. Suitable for Grades 7-9.

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