%5E6.jpeg "(2x^3y)^6")
Simplifying (2x^3y)^6
This article explores how to simplify the expression (2x^3y)^6.
Understanding Exponent Rules
Before diving into the simplification, let's recall some key exponent rules that will be used:
- Product of powers: (a^m)^n = a^(m*n)
- Power of a product: (ab)^n = a^n * b^n
Simplifying the Expression
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Apply the power of a product rule: (2x^3y)^6 = 2^6 * (x^3)^6 * y^6
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Apply the product of powers rule: 2^6 * (x^3)^6 * y^6 = 64 * x^(3*6) * y^6
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Simplify: 64 * x^(3*6) * y^6 = 64x^18y^6
Final Result
Therefore, the simplified form of (2x^3y)^6 is 64x^18y^6.
Key Takeaways
- Applying the correct exponent rules is crucial for simplifying expressions.
- Remember to distribute the exponent to each factor within the parentheses.
- Pay close attention to the power of each variable and constant.