Question 1

Which of the following multiplication will result in 6¹⁰ ?

I.   6² x 6⁸

II.  6¹⁵ ÷ 6⁵

III. 2² x 3⁵

IV.  (6⁵)²

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

Select and check your answer...

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

Let's take a look at:  I. 6² x 6⁸

Using the 1^st law, multiplying 6² with 6⁸ gives
6^{2 + 8}.

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

Therefore I. is a valid choice.

Let's take a look at:  II. 6¹⁵ ÷ 6⁵

Using the 2^nd law, dividing 6¹⁵ with 6⁵ gives
6^{15 - 5}.

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

Therefore II. is a valid choice.

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.

Let's take a look at:  IV. (6⁵)²

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

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

Therefore IV. is a valid choice.

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

Clearly, the answer is C.