%5E5.jpeg "(6x^3y^3)^5")
Simplifying the Expression (6x³y³)^5
In mathematics, simplifying expressions often involves applying the rules of exponents. Let's explore how to simplify the expression (6x³y³)^5.
Understanding the Rules of Exponents
We'll utilize the following key exponent rules:
- 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: (6x³y³)^5 = 6^5 * (x³)^5 * (y³)^5
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Apply the Power of a Power rule: 6^5 * (x³)^5 * (y³)^5 = 6^5 * x^(35) * y^(35)
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Simplify the exponents: 6^5 * x^(35) * y^(35) = 7776 * x^15 * y^15
Final Result
Therefore, the simplified expression for (6x³y³)^5 is 7776x^15y^15.