%5E4.jpeg "(2x^4y^3)^4")
Simplifying the Expression: (2x^4y^3)^4
In mathematics, we often encounter expressions involving exponents and variables. Understanding the rules of exponents is crucial for simplifying such expressions. Let's delve into simplifying the expression (2x^4y^3)^4.
Understanding the Rules of Exponents
To simplify this expression, we need to apply a few key 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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Apply the power of a product rule: (2x^4y^3)^4 = 2^4 * (x^4)^4 * (y^3)^4
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Apply the power of a power rule: 2^4 * (x^4)^4 * (y^3)^4 = 2^4 * x^(44) * y^(34)
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Simplify: 2^4 * x^(44) * y^(34) = 16x^16y^12
Final Result
Therefore, the simplified form of (2x^4y^3)^4 is 16x^16y^12.
By applying the rules of exponents systematically, we can efficiently simplify complex expressions like this one. This understanding is fundamental to various mathematical concepts and applications.