https://file.aiquickdraw.com/mathbot/file/1725891928548o360c6ol.jpg

The expression in the image is:

\[
\frac{(4p^4)^3}{8p^3}
\]

Let's simplify this step by step:

1. Expand the numerator:
   \[
   (4p^4)^3 = 4^3 \cdot (p^4)^3 = 64 \cdot p^{12}
   \]
   So the expression becomes:
   \[
   \frac{64p^{12}}{8p^3}
   \]

2. Simplify the constants:
   \[
   \frac{64}{8} = 8
   \]
   So the expression becomes:
   \[
   8 \cdot \frac{p^{12}}{p^3}
   \]

3. Simplify the powers of \(p\):
   \[
   \frac{p^{12}}{p^3} = p^{12 - 3} = p^9
   \]

Thus, the simplified expression is:
\[
8p^9
\]

Would you like more details or have any questions?

Here are some related questions:
1. What are the properties of exponents?
2. How do you simplify powers of variables in fraction form?
3. What is the general rule for raising a power to another power?
4. How would this simplification change if the exponents were different?
5. How can you use exponent rules to check your work in problems like this?

**Tip:** When simplifying expressions with exponents, always apply exponent rules methodically to avoid errors!

This lesson focuses on simplifying algebraic expressions using exponent rules. We simplify (4p^4)^3 / 8p^3 step by step, applying the power and quotient rules of exponents. Learn how to correctly expand and simplify powers of variables.

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