SOLUTION
Step 1 :
In this question, we are asked to check if :
[tex]\begin{gathered} 11^{\text{5 }}.3^{4\text{ }}^{} \\ ^{} \end{gathered}[/tex]is a factor of
[tex]11^{6\text{ }}.3^2[/tex]Step 2 :
We verify this using this method :
[tex]\begin{gathered} =\frac{11^6.3^2}{11^5.3^4} \\ =11^{6-\text{ 5}}.3^{2\text{ -4}} \\ =11^1.3^{-2} \\ =\text{ 11 x }\frac{1}{3^2} \\ =\text{ }\frac{11}{9} \\ =\text{ 1 }\frac{2}{9} \end{gathered}[/tex]Step 3 :
We can see clearly that it is NOT a factor since it has a remainder.
A number, p is a factor of another number q, if p divides q to get
a whole number.
In this situation, we have a remainder of 2, disqualifying it to
being a factor.
