Exponent Law Practice Question

Quesion icon
first law of exponents
second law of exponents
third law of exponents
law of exponents
law of exponents
law of exponents
Question 1
Which of the following equations are true?

I.    (ab)0 = 1

II.   (a2b)3 = a5b3

III.  (a10b-3)0 = z0

The following pictures are the exponent laws. You can use them as reference.

Answer

Select and check your answer...
Answer icon
A. I and II
B. I and III
C. I, II and III
D. All of the above
Check Answer

Step by Step Solution 

Solution icon
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.
'a' to the power of zero equals to 1
Solution icon
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.
This exponent law doesn't seems to fit
Solution icon
Step 3
Now, we know that:

              (a2b)3 = (a2b)(a2b)(a2b)
                       = a6b3

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                           
Newly formulated exponent law
Solution icon
Step 4
Anyway, since we already found that: 

                    (a2b)3 = a6b3

The equation II. (a2b)3 = a5b3 is false.     
Solution icon
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.
'a' to the power of zero equals to 1
Solution icon
Step 6
From Step 1 to Step 5. The valid choices are I and III.

Clearly, the answer is B.
Show Step 1
Hide This Step