%5E3.jpeg "(6a^2b^6)^3")
Simplifying (6a^2b^6)^3
This expression involves the power of a product and the power of a power. Let's break down the simplification step by step:
Understanding the Rules
- Power of a product: (xy)^n = x^n * y^n
- Power of a power: (x^m)^n = x^(m*n)
Applying the Rules
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Distribute the exponent to each factor inside the parenthesis: (6a^2b^6)^3 = 6^3 * (a^2)^3 * (b^6)^3
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Simplify each term: 6^3 = 216 (a^2)^3 = a^(23) = a^6 (b^6)^3 = b^(63) = b^18
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Combine the simplified terms: 216 * a^6 * b^18
Final Result
Therefore, the simplified form of (6a^2b^6)^3 is 216a^6b^18.