Simplifying Expressions with Exponents: (m^5n^3)^7 * m^2n
This article will guide you through simplifying the expression (m^5n^3)^7 * m^2n. We'll break down the process stepbystep, using the fundamental rules of exponents.
Understanding the Rules
Before we begin, let's recall some key exponent rules:
 Product of Powers: x^m * x^n = x^(m+n)
 Power of a Power: (x^m)^n = x^(m*n)
 Power of a Product: (x*y)^n = x^n * y^n
Simplifying the Expression

Apply the Power of a Power Rule: (m^5n^3)^7 = m^(57) * n^(37) = m^35 * n^21

Apply the Product of Powers Rule: m^35 * n^21 * m^2n = m^(35+2) * n^(21+1) = m^37 * n^22
Final Result
Therefore, the simplified expression is m^37 * n^22.
Key Takeaways
 By applying the rules of exponents, we can efficiently simplify expressions involving powers.
 Understanding these rules allows for a deeper understanding of mathematical relationships.
 Remember to always focus on the individual components and apply the rules systematically.