https://file.aiquickdraw.com/mathbot/file/1726152936257ksdtks8q.jpg

The expression in the image is:

\[
(x^2y^3z)(x^3yz^2)
\]

We can simplify this expression by applying the product of powers rule, which states that when multiplying terms with the same base, you add the exponents.

Let's break it down:

1. For \(x^2\) and \(x^3\), add the exponents:
   \[
   x^2 \cdot x^3 = x^{2+3} = x^5
   \]

2. For \(y^3\) and \(y\), the second \(y\) can be written as \(y^1\), so:
   \[
   y^3 \cdot y^1 = y^{3+1} = y^4
   \]

3. For \(z\) and \(z^2\), the first \(z\) can be written as \(z^1\), so:
   \[
   z^1 \cdot z^2 = z^{1+2} = z^3
   \]

Thus, the simplified expression is:

\[
x^5y^4z^3
\]

Would you like further details or have any questions?

Here are 5 related questions:
1. How would you simplify an expression with negative exponents, like \(x^{-2}y^3 \cdot x^3y^{-1}\)?
2. Can you explain the difference between multiplying and dividing terms with exponents?
3. How does the product of powers rule differ from the power of a power rule?
4. How would the expression change if there were fractional exponents involved?
5. What happens when you multiply expressions that include coefficients, like \(2x^2y^3 \cdot 3x^3yz\)?

**Tip**: Always apply the rule that when multiplying terms with the same base, you add the exponents, regardless of whether the exponents are positive, negative, or fractions.

Learn how to simplify the algebraic expression (x^2 y^3 z)(x^3 yz^2) by applying exponent rules. This problem demonstrates how to multiply terms with the same base and add exponents. Suitable for students in Grades 8-10.

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