Simplifying Exponential Expressions: (m^5n^3)^7 x^2n
This article will guide you through simplifying the expression (m^5n^3)^7 x^2n. We'll break down the steps using the rules of exponents.
Understanding the Rules
 Power of a product: (ab)^n = a^n * b^n
 Power of a power: (a^m)^n = a^(m*n)
Applying the Rules

Simplify the first term: (m^5n^3)^7
 Apply the "power of a product" rule: (m^5n^3)^7 = (m^5)^7 * (n^3)^7
 Apply the "power of a power" rule: (m^5)^7 * (n^3)^7 = m^(57) * n^(37) = m^35 * n^21

Combine the simplified first term with the second term:
 Now we have: m^35 * n^21 * x^2n
The Simplified Expression
Therefore, the simplified form of the expression (m^5n^3)^7 x^2n is m^35 * n^21 * x^2n.
Key Takeaways
 When simplifying expressions with exponents, remember the fundamental rules.
 Break down complex expressions into smaller parts for easier manipulation.
 Always strive to present your answer in the most simplified form.