Simplifying the Expression (x³y²)^3
In mathematics, simplifying expressions often involves applying various rules of exponents. This article will focus on simplifying the expression (x³y²)^3.
Understanding the Rules of Exponents
To understand how to simplify this expression, we need to know a few key rules of exponents:
 Product of powers: When multiplying powers with the same base, add the exponents: x<sup>m</sup> * x<sup>n</sup> = x<sup>m+n</sup>
 Power of a power: When raising a power to another power, multiply the exponents: (x<sup>m</sup>)<sup>n</sup> = x<sup>m*n</sup>
Simplifying (x³y²)^3

Applying the power of a power rule: We apply this rule to both terms inside the parentheses:
 (x³)^3 = x<sup>3*3</sup> = x<sup>9</sup>
 (y²)^3 = y<sup>2*3</sup> = y<sup>6</sup>

Combining the simplified terms: Now we have: x<sup>9</sup>y<sup>6</sup>
The Final Result
Therefore, the simplified form of (x³y²)^3 is x<sup>9</sup>y<sup>6</sup>.