%5E3-simplified.jpeg "(4x^3)^3 Simplified")
Simplifying (4x^3)^3
In this article, we'll explore how to simplify the expression (4x^3)^3.
Understanding the Properties of Exponents
To simplify this expression, we'll use the following properties of exponents:
- Power of a product: (ab)^n = a^n * b^n
- Power of a power: (a^m)^n = a^(m*n)
Applying the Properties
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Distribute the exponent: Using the power of a product property, we can rewrite the expression as: (4x^3)^3 = 4^3 * (x^3)^3
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Simplify the powers: Now, using the power of a power property, we get: 4^3 * (x^3)^3 = 64 * x^(3*3)
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Final simplification: This simplifies to: 64 * x^(3*3) = 64x^9
Conclusion
Therefore, the simplified form of (4x^3)^3 is 64x^9. By applying the properties of exponents, we can effectively simplify complex expressions.