%5E3.jpeg "(-3ab^2)^3")
Simplifying (-3ab^2)^3
In this article, we'll explore the process of simplifying the expression (-3ab^2)^3.
Understanding the Properties
To simplify this expression, we need to understand a few key 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: (-3)^3 * a^3 * (b^2)^3
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Simplify the exponents: Using the power of a power property, we simplify the expression further: -27 * a^3 * b^(2*3)
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Final result: The simplified expression is -27a^3b^6.
Conclusion
By applying the properties of exponents, we successfully simplified the expression (-3ab^2)^3 to -27a^3b^6. This process highlights the importance of understanding how exponents work and how to apply them effectively in simplifying algebraic expressions.