##### What is Exponent?

The base n raised to the power of a is equal to the multiplication of **n, a** times:

n^{a}= n × n × … × n (a times)

There:

- “n” is the
**base**and - “a” is the
**exponent**

**or**

An exponent refers to the number of times a number is multiplied by itself.

**An example of exponent**

3 to the 4th, written as **3 ^{4}** means:

3^{4}is not equal to 34 = 12

**Special Cases**

**Exponent is 0:**

n^{0}= 1

When the exponent is * zero*, as in

**5**, the result is always equal to

^{0}**1**.

5^{0}= 1

26,981^{0}= 1

**2.Exponent is negative**

n^{-a}= 1 / n^{a}

When an exponent is a negative integer, the result will always be a fraction. Fractions contain a numerator and a denominator. In this case, the numerator is always 1. To calculate the denominator, assume that the negative exponent is positive, and raise the number to that power, like this:

5^{-4}= 1 / 5^{4}

**Some Important Rules for Exponents**

**Product rule with the same base**

n^{a}.n^{b}= n^{a+b}

**Example:**

**4 ^{5} . 4^{6} = 4 ^{5+6 }= 4 ^{11} = 4194304**

**Product rule with the same exponent**

n^{a}. m^{a}= (n.m)^{a}

**Example:**

**2**^{6}. 3^{6}= (2**3)**^{6}= 6^{6}= 36

**Quotient rule with the same base**

n^{a}/ n^{b}= n^{a-b}

**Example:**

**4 ^{6} / 4^{5} = 4^{6-5 }= 4^{1} = 4**

**Quotient rule with the same exponent**

n^{a}/ m^{a}= (n/m)^{a}

**Example:**

**10 ^{6} / 5^{6} = (10/5)^{6} = 2^{6 }= 64**

** **

**Power rules #1**

(n^{a})^{b}= n^{a.b}

**Example**

**(3 ^{2})^{3 }= 3^{2*3} = 3^{6} = 729**

**Power rule 2**

**Example**

** = 4 ^{(2^3)} = 4^{8} = 6561**

**Power rule with radicals**

** **

**Example**

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