(3x^2y^3)^2 ^3

Jasonbradley

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Jun 16, 2024

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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

1. Start with the inner exponent: (3x²y³)² = (3x²y³) * (3x²y³)

2. Distribute the exponent: (3x²y³) * (3x²y³) = 3² * (x²)² * (y³)²

3. Simplify the exponents: 3² * (x²)² * (y³)² = 9x⁴y⁶

4. Now, raise the result to the outer exponent: (9x⁴y⁶)³ = 9³ * (x⁴)³ * (y⁶)³

5. Simplify further: 9³ * (x⁴)³ * (y⁶)³ = 729x¹²y¹⁸

Final Result

Therefore, the simplified form of the expression (3x²y³)²³ is 729x¹²y¹⁸.