%5E2.jpeg "(3x^4y^5)^2")
Simplifying the Expression (3x^4y^5)^2
This article will guide you through the steps to simplify the expression (3x^4y^5)^2.
Understanding the Properties
The key to simplifying this expression lies in understanding the properties of exponents:
- Power of a product: (ab)^n = a^n * b^n
- Power of a power: (a^m)^n = a^(m*n)
Simplifying the Expression
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Apply the power of a product property: (3x^4y^5)^2 = 3^2 * (x^4)^2 * (y^5)^2
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Apply the power of a power property: 3^2 * (x^4)^2 * (y^5)^2 = 9 * x^(42) * y^(52)
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Simplify the exponents: 9 * x^(42) * y^(52) = 9x^8y^10
Conclusion
Therefore, the simplified form of (3x^4y^5)^2 is 9x^8y^10.
By applying the properties of exponents, we can effectively simplify expressions like this, making them easier to understand and work with.