(3m^4)^2

Jasonbradley

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Jun 16, 2024

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Simplifying (3m^4)^2

In mathematics, simplifying expressions is a fundamental skill. One common type of simplification involves raising an expression to a power. Let's break down how to simplify the expression (3m^4)^2.

Understanding the Rules

The key to simplifying this expression lies in two fundamental rules of exponents:

• Power of a product: (ab)^n = a^n * b^n
• Power of a power: (a^m)^n = a^(m*n)

Applying the Rules

1. Apply the power of a product rule: (3m^4)^2 = 3^2 * (m^4)^2

2. Apply the power of a power rule: 3^2 * (m^4)^2 = 9 * m^(4*2)

3. Simplify: 9 * m^(4*2) = 9m^8

Conclusion

Therefore, the simplified form of (3m^4)^2 is 9m^8. Understanding and applying the rules of exponents allows us to efficiently manipulate and simplify expressions like this one.