https://file.aiquickdraw.com/mathbot/file/1726155185612h62g1sju.jpg

The expression given is:

\[
\frac{(x^3)^6}{x^5}
\]

To simplify this expression, we can use the power rule of exponents, which states that \((a^m)^n = a^{m \times n}\), and the division rule of exponents, which states that \(\frac{a^m}{a^n} = a^{m-n}\).

### Step-by-step Solution:

1. Simplify the numerator using the power rule:

   \[
   (x^3)^6 = x^{3 \times 6} = x^{18}
   \]

2. Now, rewrite the entire expression:

   \[
   \frac{x^{18}}{x^5}
   \]

3. Simplify using the division rule of exponents:

   \[
   x^{18 - 5} = x^{13}
   \]

### Final Answer:

\[
\frac{(x^3)^6}{x^5} = x^{13}
\]

Would you like more details or have any questions?

### Related Questions:

1. How do you simplify expressions with fractional exponents?
2. What are the rules for simplifying negative exponents?
3. How do you simplify expressions with different bases?
4. How do you factor expressions involving exponents?
5. What is the difference between the power rule and the product rule of exponents?

**Tip:** Always simplify powers inside parentheses before applying other exponent rules to avoid mistakes.

Learn how to simplify the expression (x^3)^6 / x^5 using the laws of exponents. This problem introduces key exponentiation concepts, applying both the power rule and the division rule. Suitable for students in Grades 8-10.

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