(m^4n^6)^4(m^3n^2p^5)^6

Jasonbradley

2 min read

·

Jun 16, 2024

23

Share

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

1. 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

2. 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.