%5E3.jpeg "(3m^2n^4)^3")
Simplifying (3m^2n^4)^3
In mathematics, simplifying expressions is a fundamental skill. Let's break down how to simplify the expression (3m^2n^4)^3.
Understanding the Laws of Exponents
To simplify this expression, we need to recall the following laws of exponents:
- Power of a product: (ab)^n = a^n * b^n
- Power of a power: (a^m)^n = a^(m*n)
Applying the Laws
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Apply the power of a product rule:
(3m^2n^4)^3 = 3^3 * (m^2)^3 * (n^4)^3
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Apply the power of a power rule:
3^3 * (m^2)^3 * (n^4)^3 = 27 * m^(23) * n^(43)
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Simplify:
27 * m^(23) * n^(43) = 27m^6n^12
Conclusion
Therefore, the simplified form of (3m^2n^4)^3 is 27m^6n^12. Understanding the laws of exponents is crucial for simplifying expressions involving powers and products of variables.