%5E2.jpeg "(6x^9y^5)^2")
Simplifying Expressions: (6x^9y^5)^2
In mathematics, simplifying expressions is a fundamental skill. Let's explore how to simplify the expression (6x^9y^5)^2.
Understanding the Rules
To simplify this expression, we need to recall the following rules:
- 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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Apply the power of a product rule: (6x^9y^5)^2 = 6^2 * (x^9)^2 * (y^5)^2
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Apply the power of a power rule: 6^2 * (x^9)^2 * (y^5)^2 = 36 * x^(92) * y^(52)
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Simplify: 36 * x^(92) * y^(52) = 36x^18y^10
Final Answer
Therefore, the simplified form of (6x^9y^5)^2 is 36x^18y^10.
Key Takeaways
- Remember the rules of exponents for simplifying expressions involving powers.
- Applying the rules step-by-step can make complex expressions easier to manage.
- Practice these rules to develop proficiency in simplifying various mathematical expressions.