### Exponent Law Practice Question #### Question 1

Which of the following equations are true?

1. (ab)0 = 1
2. (a2b)3 = a5b2
3. (a10b-3)0 = z0

The following pictures are the exponent laws. You can use them as reference.      ### Answer #### Select and check your answer...

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

### Step by Step Solution

• #### Step 1

Let's take a look at: I. (ab)0 = 1

We can treat ab as 'some number'. So, this term becomes:

(some number)0

Referring to the law as shown in the picture, we can see that (some number)0 is equals to 1.

Therefore, I. is true. • #### Step 2

Let's take a look at: II. (a2b)3 = a5b3

Oops! It seems that (a2b)3 doesn't fit into the exponent law as shown in the picture.

However, if we understand the logic behind the exponent laws, we can derive our own formula.

The following step will show you how. • #### Step 3

Now, we know that: Now, realize that you can also get a6b3 by:

a6b3 = a2x3 b1x3

With this, we can see that: (a2b1)3 = a2x3 b1x3

Therefore, we can formulate: (anbm)p = anp bmp

*Note that b = b1 • #### Step 4

Anyway, since we already found that:

(a2b)3 = a6b3

The equation II. (a2b)3 = a5b3 is false.

• #### Step 5

Let's take a look at: III. (a10b-3)0 = z0

Again, we can treat a10b-3 as 'some number'. So this term becomes:

(some number)0

Referring to the law as shown in the picture, we can see that (some number)0 is equals to 1.

Now, z0 is also equals to 1. So, the equation becomes: 1 = 1

Therefore, III. is true. • #### Step 6

From Step 1 to Step 5. The valid choices are I and III.

Clearly, the answer is B.