%5E3.jpeg "(3x^4y^2)^3")
Simplifying Expressions with Exponents: (3x^4y^2)^3
In mathematics, simplifying expressions can often involve working with exponents. One common type of problem is simplifying expressions that involve raising a product to a power. Let's look at the expression (3x^4y^2)^3.
Understanding the Rules of Exponents
The key to simplifying this expression lies in understanding the following rules of exponents:
- Power of a product: (ab)^n = a^n * b^n
- Power of a power: (a^m)^n = a^(m*n)
Simplifying the Expression
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Apply the power of a product rule: (3x^4y^2)^3 = 3^3 * (x^4)^3 * (y^2)^3
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Apply the power of a power rule: 3^3 * (x^4)^3 * (y^2)^3 = 27 * x^(43) * y^(23)
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Simplify: 27 * x^(43) * y^(23) = 27x^12y^6
Conclusion
By applying the rules of exponents, we have successfully simplified the expression (3x^4y^2)^3 to 27x^12y^6. This process demonstrates how understanding the properties of exponents can be used to manipulate and simplify complex mathematical expressions.