Question

Is 11^5 • 3^4 a factor of 11^6 • 3^2? explain why or why not.

Answer 1

Step 1 :

In this question, we are asked to check if :

`\begin{gathered} 11^{\text{5 }}.3^{4\text{ }}^{} \\ ^{} \end{gathered}`

is a factor of

`11^{6\text{ }}.3^2`

Step 2 :

We verify this using this method :

`\begin{gathered} =(11^6.3^2)/(11^5.3^4) \\ =11^{6-\text{ 5}}.3^{2\text{ -4}} \\ =11^1.3^(-2) \\ =\text{ 11 x }(1)/(3^2) \\ =\text{ }(11)/(9) \\ =\text{ 1 }(2)/(9) \end{gathered}`

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.