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Let's go through the questions one by one:

### 9) \( 2m^2 \cdot 4m^{\frac{3}{2}} \cdot 4m^{-2} \)

We will combine like terms for the powers of \( m \).

1. Multiply the coefficients: 
   \( 2 \times 4 \times 4 = 32 \)

2. Add the exponents of \( m \):
   \( 2 + \frac{3}{2} + (-2) = \frac{4}{2} + \frac{3}{2} - \frac{4}{2} = \frac{3}{2} \)

Thus, the expression simplifies to:
\[
32m^{\frac{3}{2}}
\]

---

### 11) \( \left( \frac{1}{p^{\frac{3}{2}}} \right)^{-2} \)

To simplify this, we apply the exponent rule \( (a^m)^n = a^{m \cdot n} \):

1. Apply the power to both the numerator and denominator: 
   \[
   \left( p^{-\frac{3}{2}} \right)^{-2} = p^{\left( -\frac{3}{2} \times -2 \right)} = p^3
   \]

Thus, the simplified result is:
\[
p^3
\]

---

### 13) \( \frac{2x^{\frac{7}{4}}}{4x^{\frac{4}{3}}} \)

We will divide the coefficients and subtract the exponents of \( x \).

1. Divide the coefficients: 
   \( \frac{2}{4} = \frac{1}{2} \)

2. Subtract the exponents of \( x \): 
   \( \frac{7}{4} - \frac{4}{3} = \frac{21}{12} - \frac{16}{12} = \frac{5}{12} \)

Thus, the expression simplifies to:
\[
\frac{1}{2} x^{\frac{5}{12}}
\]

---

Would you like more details on any of these steps, or have further questions?

Here are five related questions for further practice:
1. Simplify \( (3x^4)(x^{-2})(5x^3) \).
2. Simplify \( \frac{6x^{\frac{5}{2}}}{9x^{\frac{3}{2}}} \).
3. Simplify \( \left( \frac{2}{x^{3/2}} \right)^{-1} \).
4. Solve \( (5a^2)(2a^{-1})(a^{\frac{1}{2}}) \).
5. Simplify \( \frac{8y^{7/3}}{2y^{4/3}} \).

**Tip**: When simplifying expressions with exponents, always remember to handle coefficients separately from the variables.

Simplify the following expressions: 9) 2m^2 * 4m^(3/2) * 4m^(-2) 11) (1 / p^(3/2))^(-2) 13) (2x^(7/4)) / (4x^(4/3))

This problem involves simplifying expressions with exponents using exponent rules such as multiplication and division of powers. Learn how to apply the laws of exponents to expressions like 2m^2 * 4m^(3/2) * 4m^(-2) and (2x^(7/4)) / (4x^(4/3)) with step-by-step solutions. Suitable for high school students in Grades 9-12.

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