%5E3.jpeg "(4x^3y^3)^3")
Simplifying (4x^3y^3)^3
In mathematics, simplifying expressions is a crucial skill. Let's tackle the simplification of (4x^3y^3)^3.
Understanding the Concepts
- Exponents: An exponent indicates the number of times a base is multiplied by itself. For example, x^3 means x * x * x.
- Power of a product: When a product is raised to a power, each factor within the product is raised to that power.
- Power of a power: When a power is raised to another power, you multiply the exponents.
Applying the Rules
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Distribute the exponent: We apply the power of a product rule to distribute the exponent of 3 to each factor within the parentheses: (4x^3y^3)^3 = 4^3 (x^3)^3 (y^3)^3
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Simplify the exponents: Using the power of a power rule, we multiply the exponents: 4^3 (x^3)^3 (y^3)^3 = 64x^9y^9
The Simplified Form
Therefore, the simplified form of (4x^3y^3)^3 is 64x^9y^9.
Key Takeaways
- Simplifying expressions involves understanding and applying fundamental exponent rules.
- The power of a product rule allows us to distribute exponents to each factor.
- The power of a power rule enables us to multiply exponents when a power is raised to another power.