The expression you've given is \( 4p \cdot 3p^{\frac{5}{4}} \).

To simplify this, follow these steps:

1. Multiply the constants \(4\) and \(3\) first: 
   \[
   4 \cdot 3 = 12
   \]
2. Now, apply the product of powers rule \( p^a \cdot p^b = p^{a+b} \):
   \[
   p \cdot p^{\frac{5}{4}} = p^{1 + \frac{5}{4}} = p^{\frac{9}{4}}
   \]
3. Combine the result:
   \[
   12p^{\frac{9}{4}}
   \]

Thus, the simplified expression is:
\[
12p^{\frac{9}{4}}
\]

Would you like more details or have any questions? 

Here are some related questions for practice:
1. Simplify \( 2x \cdot 5x^{\frac{3}{2}} \).
2. What is the result of \( 7y \cdot 4y^{\frac{2}{3}} \)?
3. How do you simplify \( p^2 \cdot p^{\frac{1}{2}} \)?
4. Simplify \( 6p^3 \cdot 2p^{\frac{7}{2}} \).
5. What is the simplified form of \( x \cdot 3x^{4} \)?

**Tip**: When multiplying powers with the same base, just add their exponents!

Learn how to simplify the expression 4p ⋅ 3p^(5/4) using exponent rules. This step-by-step solution applies the product of powers rule and is suitable for students in Grades 9-11.

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