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Simplifying (2x³y⁵)⁵
In mathematics, simplifying expressions is a crucial step in solving equations and understanding their properties. Let's examine how to simplify the expression (2x³y⁵)⁵.
Understanding the Rules of Exponents
The expression involves raising a product of variables and constants to a power. We can simplify this expression by using the following rules of exponents:
- Product of powers: (a * b)ⁿ = aⁿ * bⁿ
- Power of a power: (aⁿ)ᵐ = aⁿᵐ
Applying the Rules
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Apply the product of powers rule: (2x³y⁵)⁵ = 2⁵ * (x³)⁵ * (y⁵)⁵
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Apply the power of a power rule: 2⁵ * (x³)⁵ * (y⁵)⁵ = 32 * x¹⁵ * y²⁵
Final Result
Therefore, the simplified form of (2x³y⁵)⁵ is 32x¹⁵y²⁵.
Key Points to Remember
- Exponents indicate repeated multiplication. For instance, x⁵ means x * x * x * x * x.
- Always follow the order of operations (PEMDAS/BODMAS) when simplifying expressions.
- Understanding exponent rules is essential for working with various mathematical concepts.