### Exponent Laws Practice Question

#### Question 1

Which of the following multiplication will result in 610 ?

1. 62 x 68
2. 615 ÷ 65
3. 22 x 35
4. (65)2

The following pictures are the first, second and third law of exponents respectively. You can use them as reference.

A. I, II and III
B. II, III and IV
C. I, II and IV
D. All of the above

### Step by Step Solution

• #### Step 1

Let's take a look at: I. 62 x 68

Using the 1st law, multiplying 62 with 68 gives 62 + 8.

• #### Step 2

Now, by adding the exponents, 2 with 8, we get 10. This gives 610.

Therefore I. is a valid choice.

• #### Step 3

Let's take a look at: II. 615 ÷ 65

Using the 2nd law, dividing 615 with 65 gives 615 - 5.

• #### Step 4

Now, minus the exponents, 15 with 5, we get 10. This gives 610.

Therefore II. is a valid choice.

• #### Step 5

Let's take a look at: III. 22 x 35

For these terms, the base is not the same number. Now, looking at the first law, it requires the base to be the same.

Therefore III. is not a valid choice.

• #### Step 6

Let's take a look at: IV. (65)2

Using the 3rd law, multiplying the exponents 5 and 2 gives 6 5 x 2.

• #### Step 7

Now, 5 multiply by 2 gives 10. So we have 610.

Therefore IV. is a valid choice.

• #### Step 8

From step 1 to step 7. The valid choices are I, II and IV.