Math Expression: Exponent Laws Practice Questions

Which of the following multiplication will result in 6¹⁰ ?

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

Step 1

Let's take a look at: I. 6² x 6⁸

Using the 1st law, multiplying 6² with 6⁸ gives 6^{2 + 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 2^nd law, dividing 6¹⁵ with 6⁵ gives 6^{15 - 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 3^rd 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.