%5E3.jpeg "(5x^2y)^3")
Simplifying (5x^2y)^3
In mathematics, simplifying expressions is a crucial skill. One common type of expression involves exponents, especially when dealing with parentheses. Let's explore how to simplify the expression (5x^2y)^3.
Understanding the Rules
The key to simplifying this expression lies in understanding the following 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
Let's apply these rules to our expression:
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Power of a product: First, we apply the power of a product rule to the entire expression within the parentheses: (5x^2y)^3 = 5^3 * (x^2)^3 * y^3
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Power of a power: Now, we apply the power of a power rule to the x term: 5^3 * (x^2)^3 * y^3 = 5^3 * x^(2*3) * y^3
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Simplify: Finally, we simplify the exponents and perform the multiplication: 5^3 * x^(2*3) * y^3 = 125x^6y^3
Final Result
Therefore, the simplified form of (5x^2y)^3 is 125x^6y^3.
This process demonstrates how understanding the fundamental rules of exponents allows us to simplify complex expressions efficiently.