%5E2.jpeg "(5x^4y^3)^2")
Simplifying Expressions with Exponents: (5x^4y^3)^2
In mathematics, simplifying expressions often involves working with exponents. One common operation is squaring an expression containing multiple variables and coefficients, such as (5x^4y^3)^2. Let's break down how to simplify this expression.
Understanding the Properties of Exponents
The key to simplifying this expression lies in understanding 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 property: (5x^4y^3)^2 = 5^2 * (x^4)^2 * (y^3)^2
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Apply the power of a power property: 5^2 * (x^4)^2 * (y^3)^2 = 25 * x^(42) * y^(32)
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Simplify: 25 * x^(42) * y^(32) = 25x^8y^6
Conclusion
Therefore, the simplified form of (5x^4y^3)^2 is 25x^8y^6. This process demonstrates how applying basic exponent properties allows us to efficiently simplify expressions involving multiple variables and exponents.