Question

using exponent rules, fully simplify. $(-3x^{2}y^{2})^{3}$

Explanation:

Step1: Apply power of a product rule

The power of a product rule states that \((ab)^n = a^n b^n\). So, we can apply this to \((-3x^{2}y^{2})^{3}\) as follows:
\((-3)^{3}(x^{2})^{3}(y^{2})^{3}\)

Step2: Calculate \((-3)^{3}\)

\((-3)^{3}=(-3)\times(-3)\times(-3)= -27\)

Step3: Apply power of a power rule

The power of a power rule states that \((a^m)^n=a^{m\times n}\). For \((x^{2})^{3}\), we have \(x^{2\times3}=x^{6}\). For \((y^{2})^{3}\), we have \(y^{2\times3}=y^{6}\)

Step4: Combine the results

Putting it all together, we get \(-27x^{6}y^{6}\)

Answer:

\(-27x^{6}y^{6}\)