To simplify $(6x^5y^3)^2$, apply the power rule for exponents:

$(a^m)^n = a^{m \cdot n}.$

Step-by-step solution:

1. Apply the square to each factor inside the parentheses: $(6x^5y^3)^2 = 6^2 \cdot (x^5)^2 \cdot (y^3)^2$

2. Simplify each term:

   • $6^2 = 36$,
   • $(x^5)^2 = x^{5 \cdot 2} = x^{10}$,
   • $(y^3)^2 = y^{3 \cdot 2} = y^6$.

3. Combine the results: $(6x^5y^3)^2 = 36x^{10}y^6$

Final Answer:

$36x^{10}y^6$

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Would you like more examples or a deeper explanation of exponent rules?

Here are 5 related questions for practice:

1. Simplify $(3x^4y^2)^3$.
2. Simplify $(2a^2b)^4$.
3. Expand and simplify $(5x^3y)^2(2x^2y^3)$.
4. How does the power rule apply to fractions, e.g., $(\frac{2x^3}{y})^2$?
5. What is the result of $(x^2y^3)^0$?

Tip: When working with exponents, always remember that the power rule applies to both constants and variables within the parentheses!