%5E3.jpeg "(5x^2y^2)^3")
Simplifying Expressions: (5x²y²)^3
In mathematics, simplifying expressions is a crucial skill. One common type of simplification involves expressions with exponents. Let's delve into the simplification of the expression (5x²y²)^3.
Understanding the Rules
The key to simplifying this expression lies in understanding the 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
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Distribute the exponent: Applying the power of a product rule, we get: (5x²y²)^3 = 5^3 * (x²)^3 * (y²)^3
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Simplify individual exponents: Applying the power of a power rule, we get: 5^3 * (x²)^3 * (y²)^3 = 125 * x^(23) * y^(23)
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Final simplification: 125 * x^(23) * y^(23) = 125x⁶y⁶
Conclusion
Therefore, the simplified form of (5x²y²)^3 is 125x⁶y⁶. This process highlights the importance of understanding exponent rules in simplifying complex expressions. Remember to break down the problem into smaller steps, applying the appropriate rules, and you will successfully navigate even the most intricate mathematical expressions.