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Simplifying the Expression: (3x²y³)²³
Let's break down how to simplify the expression (3x²y³)²³ step by step.
Understanding the Exponents
- ( )²³: This indicates that the entire expression inside the parentheses is being raised to the power of 23.
- (3x²y³)²: This indicates that the expression inside the parentheses is being squared, meaning multiplied by itself.
Applying the Rules of Exponents
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Start with the inner exponent: (3x²y³)² = (3x²y³) * (3x²y³)
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Distribute the exponent: (3x²y³) * (3x²y³) = 3² * (x²)² * (y³)²
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Simplify the exponents: 3² * (x²)² * (y³)² = 9x⁴y⁶
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Now, raise the result to the outer exponent: (9x⁴y⁶)³ = 9³ * (x⁴)³ * (y⁶)³
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Simplify further: 9³ * (x⁴)³ * (y⁶)³ = 729x¹²y¹⁸
Final Result
Therefore, the simplified form of the expression (3x²y³)²³ is 729x¹²y¹⁸.