%5E3.jpeg "(2v^4)^3")
Simplifying (2v^4)^3
In mathematics, simplifying expressions is a fundamental skill. This article will guide you through the process of simplifying the expression (2v^4)^3.
Understanding the Rules
The key to simplifying this expression lies in understanding the 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
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Distribute the exponent: We start by applying the power of a product rule: (2v^4)^3 = 2^3 * (v^4)^3
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Simplify the powers: Next, we apply the power of a power rule: 2^3 * (v^4)^3 = 8 * v^(4*3)
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Final simplification: 8 * v^(4*3) = 8v^12
Conclusion
Therefore, the simplified form of (2v^4)^3 is 8v^12. By understanding and applying the rules of exponents, you can confidently simplify complex expressions like this one.