### 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.

Clearly, the answer is C.