https://file.aiquickdraw.com/mathbot/file/17265512798525dgdixen.jpg

The expression shown in the image is:

\[
\left( x^{3y} \right)^{5y}
\]

To simplify this, we can apply the exponentiation rule, which states that \((a^m)^n = a^{m \cdot n}\).

Applying this to the given expression:

\[
\left( x^{3y} \right)^{5y} = x^{3y \cdot 5y} = x^{15y^2}
\]

Thus, the simplified form of the expression is:

\[
x^{15y^2}
\]

Would you like any additional details or have further questions?

Here are five related questions to consider:
1. How would you simplify an expression like \(\left( a^{2b} \right)^{3c}\)?
2. What happens if the base is a product of terms, such as \(\left( xy \right)^{5}\)?
3. Can you explain how the power of a product works in exponents?
4. What if \(x = 2\) and \(y = 1\)? How would the expression simplify numerically?
5. How would you apply the power of a power rule to a more complex base, like \(\left( x^{2y} z^3 \right)^{4y}\)?

**Tip:** Always remember to multiply exponents when raising a power to another power!

Learn how to simplify the algebraic expression (x^{3y})^{5y} using exponentiation rules. This guide breaks down the steps, including applying the power of a power rule. Ideal for high school students studying exponents and algebra.

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