Simplifying Expressions with Exponents
This article will explore the simplification of the expression (m^4n^6)^4(m^3n^2p^5)^6. We will use the rules of exponents to arrive at a simplified form.
Rules of Exponents
To simplify this expression, we need to recall a few important rules of exponents:
 Product of Powers: x^m * x^n = x^(m+n)
 Power of a Power: (x^m)^n = x^(m*n)
Simplifying the Expression

Apply the Power of a Power Rule:
 (m^4n^6)^4 = m^(44)n^(64) = m^16n^24
 (m^3n^2p^5)^6 = m^(36)n^(26)p^(5*6) = m^18n^12p^30

Apply the Product of Powers Rule:
 m^16n^24 * m^18n^12p^30 = m^(16+18)n^(24+12)p^30 = m^34n^36p^30
Final Answer
Therefore, the simplified form of the expression (m^4n^6)^4(m^3n^2p^5)^6 is m^34n^36p^30.