Question 2

Simplify the following expression:








The following pictures are the exponent laws. You can use them as reference.

Select and check your answer...

A. 3s
B. 3qs
C. 3q
D. 3q²s

Let's first focus on the numerator:

                    6(q²s³)²

Using the exponent law* as shown in the picture, we get:

          
           6(q²s³)² = 6q^{2 x 2} s^{3 x 2}


*Note: If you are not sure on how to derive this law, you can see it at step 3 in this practice question.

Now,
     2 multiply by 2  gives 4, and
     3 multiply by 2 gives 6.

Hence, we have 6p⁴s⁶.

Next, let's focus on the denominator:

                    2(qs²)³

Using the exponent law* as shown in the picture, we get:

          
           2(qs²)³ = 2q^{1 x 3} s^{2 x 3}


*Note: If you are not sure on how to derive this law, you can see it at step 3 in this practice question.

Now,
     1 multiply by 3  gives 3, and
     2 multiply by 3 gives 6.

Hence, we have 2p³s⁶.   

Now, after simplifying the numerator and denominator, the original expression becomes:
       
              6p⁴s⁶ ÷ 2p³s⁶

Using the exponent law as shown in the picture, we get:

          
           6p⁴s⁶ ÷ 2p³s⁶

         = 3q^{4 - 3} s^{6 - 6}

Simplifying,
                3q^{4 - 3} s^{6 - 6}
                 
We get:
                3q¹ s⁰       
         
Now, we can write:
               
                 q¹ as q   and,
               
                 s⁰ as 1

Finally, we have the simplest term, 3q.

Clearly, the answer is C.