%5E4.jpeg "(3x^2y^4)^4")
Simplifying Exponential Expressions: (3x^2y^4)^4
This article will explore the simplification of the exponential expression (3x^2y^4)^4.
Understanding the Properties
To simplify this expression, we'll use the following properties of exponents:
- Power of a Product: (ab)^n = a^n * b^n
- Power of a Power: (a^m)^n = a^(m*n)
Applying the Properties
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Apply the Power of a Product rule: (3x^2y^4)^4 = 3^4 * (x^2)^4 * (y^4)^4
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Apply the Power of a Power rule: 3^4 * (x^2)^4 * (y^4)^4 = 81 * x^(24) * y^(44)
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Simplify the exponents: 81 * x^(24) * y^(44) = 81x^8y^16
Conclusion
Therefore, the simplified form of the expression (3x^2y^4)^4 is 81x^8y^16.