In this article, we will discuss different laws of exponents which are important considering GMAT exam. Laws of exponents are following:

**(1)**

**(2)**

**(3)**

**(4)**

**(5)**

**(6)**

**(7)**

Now we can understand these laws one by one with the help of examples. We will refer to each law with the numbers mentioned above.

According to first law of exponents, we have

## It means that , and so on.

**Evaluate:**

** **

**Evaluate:**

Now we can try some more problems regarding first law of exponents.

**GMAT Sample Problem 9:**

### What is the value of m such that ?

**(A)** -3 **(B)** 3

**(C)** 0 **(D)** None of these

Using first law of exponents, we get

Hence, the answer is **(A)**.

**GMAT Sample Problem 10:**

What is the value of n such that ?

**(A)** 16 **(B)** 4

**(C)** -4 **(D)** None of the above

Using first law of exponents, we get

Hence, the answer is **(C)**.

We can now move to the second law of exponents. According to the second law of exponents, we have

**Example:** , and so on.

**GMAT Sample Problem 11:**

is equal to:

**(A)** **(B)**

**(C)** **(D)** None of these

Hence, the answer is **(A).**

Let's move to 3rd law of exponents. According to this law, we have

**Example:** , and so on.

**GMAT Sample Problem 12:**

What is the value of m such that ?

**(A)** -4 **(B)** 4

**(C)** 3 **(D)** None of these

**Applying 3rd law of exponents, we get**

Hence, the answer is **(B)**.

Now we will cover 4th law of exponents with the help of examples. According to 4th law of exponents, we have

**Example:** ,

**GMAT Sample Problem 13:**

is equal to:

**(A)**

**(B)**

**(C)**

**(D)** Both (B) and (C)

**(E)** Both (A) and (B)

By 4th law of exponents, we know that .

Therefore,

Note that 125 can also be written as .

Therefore,

Hence, the answer is **(D)**.

**Did this question trick you? 🙂**

Now it's the time to move to 5th law of exponents. According to this law, we have

**Example:** ,

**GMAT Sample Problem 14:**

What is the value of m such that ?

**(A)** 3 **(B)** -3

**(C)** 4 **(D)** None of these

**(5th law of exponents)**

Hence, the answer is **(A)**.

**GMAT Sample Problem 15:**

is equal to:

**(A)** **(B)**

(C) 8000 **(D)** Both (B) and (C)

**(E)** None of the above

Also, .

Hence, the answer is **(D)**.

According to 6th law of exponents, we have

**Example:** , and so on.

**GMAT Sample Problem 16:**

is equal to:

**(A)** **(B)**

**(C)** **(D)** None of these

Hence, the answer is **(C)**.

7th law of exponents is fairly simple. According to this law, we have

**Example:** and so on.

A particular GMAT problem can be based on more than one law at a time. GMAT **sample problems from 9 to 15** were based on just one law at a time. In the later articles, we will try problems which will be based on more than one law at a time.