Correct simplification of the given expression is [tex]9x^{2} y^{21}[/tex].
The given expression is:
[tex](3xy^6)^{2} (y^3)^{3}[/tex]
What is the simple form of (abc)ⁿ?
The simple form of (abc)ⁿ is aⁿbⁿcⁿ.
Same way, [tex](3xy^6)^{2} (y^3)^{3}[/tex]
= [tex]3^2 x^2 (y^6)^2 (y^3)^3[/tex].....(1)
As we know that [tex](a^m)^n = a^{mn}[/tex]
So, [tex](y^6)^2 = y^{12} \\\\[/tex] and [tex](y^3)^3 = y^9[/tex]
So (1) becomes [tex]9x^{2} y^{12} y^9[/tex]
We know that [tex]a^m a^n = a^{m+n}[/tex]
So [tex]9x^{2} y^{12} y^9[/tex] = [tex]9x^{2} y^{21}[/tex]
Therefore, correct simplification of the given expression is [tex]9x^{2} y^{21}[/tex].
To get more about exponents' rule visit:
https://brainly.com/question/15715630
