The problem in the image asks for the simplified form of the expression:

$p^{\frac{2}{3}} \cdot p^{\frac{3}{2}}$

To simplify this, we use the rule of exponents which states that when multiplying powers with the same base, we add their exponents:

$p^{\frac{2}{3}} \cdot p^{\frac{3}{2}} = p^{\frac{2}{3} + \frac{3}{2}}$

Now, we need to add the fractions $\frac{2}{3}$ and $\frac{3}{2}$. To do this, we first find a common denominator. The least common denominator between 3 and 2 is 6, so we rewrite the fractions as:

$\frac{2}{3} = \frac{4}{6}, \quad \frac{3}{2} = \frac{9}{6}$

Now, adding them together:

$\frac{4}{6} + \frac{9}{6} = \frac{13}{6}$

Thus, the simplified form of the expression is:

$p^{\frac{13}{6}}$

Would you like more details or explanations about any part of this? Here are some related questions to explore:

1. How do you simplify expressions with fractional exponents?
2. What is the general rule for multiplying powers with the same base?
3. How do you find the least common denominator of two fractions?
4. Can you explain how to convert mixed fractions to improper fractions?
5. How would the answer change if the base were different?

Tip: When dealing with exponents, always remember the basic exponent rules (product, quotient, and power rules) to simplify the expressions efficiently.