### Exponent Laws Questions

#### Question 2

Simplify the following expression:

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

A. 3s
B. 3qs
C. 3q
D. 3q2s

### Step by Step Solution

• #### Step 1

Let's first focus on the numerator:

6(q2s3)2

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

6(q2s3)2 = 6q2 x 2 s3 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.

• #### Step 2

Now,

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

Hence, we have 6q4s6.

• #### Step 3

Next, let's focus on the denominator:

2(qs2)3

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

2(qs2)3 = 2q1 x 3 s2 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.

• #### Step 4

Now,

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

Hence, we have 2q3s6.

• #### Step 5

Now, after simplifying the numerator and denominator, the original expression becomes:

6q4s6 ÷ 2q3s6
• #### Step 6

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

6q4s6 ÷ 2q3s6
= 3q4 - 3 s6 - 6
• #### Step 7

Simplifying,

3q4 - 3 s6 - 6

We get:

3q1 s0

Now, we can write:

q1 as q and,
s0 as 1
• #### Step 8

Finally, we have the simplest term, 3q