%5E3.jpeg "(2x^2y^4)^3")
Simplifying the Expression (2x^2y^4)^3
In mathematics, simplifying expressions is a crucial skill. Let's break down how to simplify the expression (2x^2y^4)^3.
Understanding the Properties of Exponents
The key to simplifying this expression lies in understanding the properties of exponents. Here are the relevant properties:
- 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: We can distribute the exponent 3 to both the coefficient (2) and the variables (x^2 and y^4). This gives us:
(2x^2y^4)^3 = 2^3 * (x^2)^3 * (y^4)^3
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Apply the Power of a Power Property: Now we multiply the exponents for the variables.
2^3 * (x^2)^3 * (y^4)^3 = 2^3 * x^(23) * y^(43)
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Simplify: Finally, we calculate the values.
2^3 * x^(23) * y^(43) = 8x^6y^12
Conclusion
Therefore, the simplified form of (2x^2y^4)^3 is 8x^6y^12. By understanding and applying the properties of exponents, we can efficiently simplify complex expressions.