Answer :
[tex]\frac{1}{16y^{28}}[/tex]
STEP - BY - STEP EXPLANATION
What to find?
The solution to the system of equation.
Given:
(12y¹¹ /6 y⁴)⁻⁴
[tex](\frac{12y^{11}}{6y^4})^{-4}[/tex]To solve the given problem, we will follow the steps below:
Step 1
Recall the law of indices that is applicable.
That is;
[tex]\begin{gathered} \frac{a^3^{}^{}^{}}{a^2}=a^{3-2} \\ \\ a^{-2}=\frac{1}{a^2} \end{gathered}[/tex]Step 2
Apply the first law on the given expression.
[tex]\begin{gathered} (2y^{11-4})^{-4} \\ \\ (2y^7)^{-4} \end{gathered}[/tex]Step 3
Apply the second law to the above.
[tex]=\frac{1}{(2y^7)^4}[/tex][tex]=\frac{1}{16y^{28}}[/tex]Therefore,
[tex](\frac{12y^{11}}{6y^4})^{-4}=\frac{1}{16y^{28}}[/tex]