Answer:
1. Start with the expression:
[tex]\huge\frac{2 a^{2} b^{2} \times\left(-3 a^{2} b^{2}\right)^{2}}{6 a b \times 9 a^{2} b^{2}} [/tex]
2. Simplify the numerator:
[tex]\normalsize2 a^{2} b^{2} \times\left(-3 a^{2} b^{2}\right)^{2} = 2 a^{2} b^{2} \times 9 a^{4} b^{4} = 18 a^{6} b^{6} [/tex]
3. Simplify the denominator:
[tex]6 a b \times 9 a^{2} b^{2} = 54 a^{3} b^{3} [/tex]
4. Combine the numerator and denominator:
[tex] \huge\frac{18 a^{6} b^{6}}{54 a^{3} b^{3}} [/tex]
5. Simplify the fraction:
[tex]\frac{18}{54} \times \frac{a^{6} b^{6}}{a^{3} b^{3}} = \frac{1}{3} \times a^{3} b^{3} = \frac{a^{3} b^{3}}{3} [/tex]
So, the simplified form is [tex]\frac{a^{3} b^{3}}{3}. [/tex] Therefore, I disagree with the given statement that the expression equals [tex]a^{3} b^{3}. [/tex]The correct simplified form is [tex]\frac{a^{3} b^{3}}{3}[/tex]
