%5E3-simplify.jpeg "(4ab^2)^3 Simplify")
Simplifying (4ab^2)^3
This article will guide you through the steps of simplifying the expression (4ab^2)^3.
Understanding the Properties
To simplify this expression, we will use the following properties of exponents:
- (ab)^n = a^n * b^n This property states that when raising a product to a power, we can distribute the exponent to each factor.
- (a^m)^n = a^(m*n) This property states that when raising a power to another power, we multiply the exponents.
Simplifying the Expression
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Distribute the exponent: Using the first property, we can distribute the exponent 3 to each factor inside the parentheses: (4ab^2)^3 = 4^3 * a^3 * (b^2)^3
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Simplify the powers: Now, we can simplify the powers using the second property: 4^3 * a^3 * (b^2)^3 = 64 * a^3 * b^(2*3)
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Combine the exponents: Finally, we can combine the exponents of b: 64 * a^3 * b^(2*3) = 64a^3b^6
Conclusion
Therefore, the simplified form of (4ab^2)^3 is 64a^3b^6. Remember to apply the properties of exponents correctly to arrive at the correct solution.