The image contains a set of mathematical expressions involving powers, multiplication, and division, asking to simplify each expression using the properties of exponents.

Let's go through a couple of examples from the provided image.

a. $2x^2 \cdot 3x^2 \cdot 2x$

Simplification:

1. Combine the coefficients: $2 \cdot 3 \cdot 2 = 12$.
2. For the variables, use the property $x^a \cdot x^b = x^{a+b}$: $x^2 \cdot x^2 \cdot x = x^{2+2+1} = x^5$ Thus, the simplified expression is: $12x^5$

b. $4 \cdot 2x \cdot 3x^2y^2$

Simplification:

1. Combine the constants: $4 \cdot 2 \cdot 3 = 24$.
2. Apply the exponent rule for multiplication to the $x$-terms and $y$-terms: $x \cdot x^2 = x^{1+2} = x^3$ $y^2$ remains as it is. Thus, the simplified expression is: $24x^3y^2$

Would you like me to continue with more examples, or do you want any specific expression explained in detail? Let me know if you have any questions!

Here are 5 related questions to explore:

1. How do you apply the power rule for division of exponents?
2. What is the rule for raising a product to a power?
3. How can you simplify an expression with multiple variables raised to powers?
4. How would you approach simplifying a fraction with exponents in both the numerator and denominator?
5. Can negative exponents appear in simplified form, and how do you handle them?

Tip:

When multiplying terms with exponents, remember to add the exponents if the bases are the same!