(3x^2y^5)^3

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression (3x²y⁵)³

This article will guide you through the process of simplifying the expression (3x²y⁵)³.

Understanding the Exponent

The exponent 3 outside the parentheses means that the entire expression within the parentheses is multiplied by itself three times. This can be written as:

(3x²y⁵)³ = (3x²y⁵) * (3x²y⁵) * (3x²y⁵)

Applying the Exponent Rules

To simplify the expression, we need to apply the following exponent rules:

• (ab)ⁿ = aⁿbⁿ: This rule states that the exponent applies to both the coefficient and the variables.
• (aⁿ)ᵐ = aⁿᵐ: This rule states that when an exponent is raised to another exponent, the exponents are multiplied.

Step-by-Step Simplification

1. Apply the first rule to each term inside the parentheses: (3x²y⁵)³ = 3³(x²)³(y⁵)³

2. Apply the second rule to each variable: 3³(x²)³(y⁵)³ = 3³x⁶y¹⁵

3. Calculate the numerical value of 3³: 3³x⁶y¹⁵ = 27x⁶y¹⁵

Final Result

Therefore, the simplified expression of (3x²y⁵)³ is 27x⁶y¹⁵.