%5E2.jpeg "(6x^3y^5)^2")
Simplifying (6x³y⁵)²
In mathematics, simplifying expressions is a crucial skill. Let's break down how to simplify the expression (6x³y⁵)².
Understanding the Concept
The expression involves a power of a product, meaning we have a product of terms raised to a power. The rule for simplifying this type of expression is:
(ab)² = a²b²
This rule essentially states that we can distribute the exponent to each term within the parentheses.
Applying the Rule
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Distribute the exponent: (6x³y⁵)² = 6² (x³)² (y⁵)²
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Simplify the exponents: 6² (x³)² (y⁵)² = 36x⁶y¹⁰
Final Answer
Therefore, the simplified form of (6x³y⁵)² is 36x⁶y¹⁰.
Key Points to Remember
- When raising a power to another power, multiply the exponents: (a^m)^n = a^(m*n).
- The exponent applies to every term inside the parentheses.
- Pay attention to the order of operations: exponents are performed before multiplication.