https://file.aiquickdraw.com/mathbot/file/172640165805080ncz4vc.jpg

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.

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### 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:
   \[
   12x^5
   \]

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### 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:
   \[
   24x^3y^2
   \]

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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!

Simplify the algebraic expressions using exponent rules.

This page covers how to simplify algebraic expressions using exponent rules, including combining like terms and applying multiplication, division, and power rules. Suitable for students in Grades 8-10.

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