%5E2.jpeg "(m^3n^4)^2")
Simplifying (m^3n^4)^2
In mathematics, simplifying expressions is a fundamental skill. One common type of simplification involves exponents. Let's explore how to simplify the expression (m^3n^4)^2.
Understanding the Rules of Exponents
To simplify this expression, we need to understand a couple of key rules about exponents:
- The Power of a Product Rule: (ab)^n = a^n * b^n
- The Power of a Power Rule: (a^m)^n = a^(m*n)
Applying the Rules
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Apply the Power of a Product Rule:
(m^3n^4)^2 = (m^3)^2 * (n^4)^2 -
Apply the Power of a Power Rule: (m^3)^2 * (n^4)^2 = m^(32) * n^(42)
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Simplify the Exponents: m^(32) * n^(42) = m^6n^8
Conclusion
Therefore, the simplified form of (m^3n^4)^2 is m^6n^8. This process demonstrates the power of applying basic exponent rules to simplify complex expressions.