%5E4.jpeg "(2a^3b^4)^4")
Simplifying the Expression: (2a^3b^4)^4
In mathematics, simplifying expressions often involves applying various rules and properties. Here, we'll break down how to simplify the expression (2a^3b^4)^4.
Understanding the Rules
- 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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Apply the power of a product rule: (2a^3b^4)^4 = 2^4 * (a^3)^4 * (b^4)^4
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Apply the power of a power rule: 2^4 * (a^3)^4 * (b^4)^4 = 16 * a^(34) * b^(44)
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Simplify the exponents: 16 * a^(34) * b^(44) = 16a^12b^16
Conclusion
Therefore, the simplified form of (2a^3b^4)^4 is 16a^12b^16. By understanding and applying the appropriate rules, we can effectively simplify complex mathematical expressions.