Exponents indicate repeated multiplication of a number by itself. There are Six Laws of Exponents in general and we have provided each scenario by considering enough examples. For instance, 5*5*5 can be expressed as 5^{3}. Here 3 indicates the number of times the number 5 is multiplied. Thus, power or exponent indicates how many times a number can be multiplied.

Usually, Exponents abide by certain rules and they are used to simplify expressions and are also called Laws. Let’s dive into the article and learn about the Exponent Laws in detail.

## Exponent Rules with Examples

There are six laws of exponents and we have stated each of them by taking examples.

- Product With the Same Bases
- Quotient with Same Bases
- Power Raised to a Power
- Product to a Power
- Quotient to a Power
- Zero Power

### Product with Same Bases

In Multiplication of Exponents with Same bases then we need to add the Exponents. We can’t add the Exponents with unlike bases.

According to this law, for any non-zero term a, we have

**a ^{m}. a^{n} = a^{m+n}** in which m, n are real numbers.

**Example**

Simplify 4^{5}.4^{2}?

**Solution:**

Given 4^{5}.4^{2}

= 4^{4+2}

= 4^{6}

Simplify (-2)^{3}. (-2)^{1}?

**Solution:**

Given (-2)^{3}.(-2)^{1}

= (-2)^{3+1}

= (-2)^{4}

### Quotient with Same Bases

In the case of the division with the same bases, we need to subtract the Exponents. According to this rule **a ^{m}/a^{n} = a^{m-n}** where a is a non zero integer and m, n are integers.

**Example**

Find the Value of 10^{-4}/10^{-2}?

**Solution:**

Given 10^{-4}/10^{-2}

= 10^{-4-(-2)}

= 10^{-4+2}

= 10^{-2}

= 1/10^{2}

= 1/100

### Power Raised to a Power

As per this law, if a is the base and then power raised to the power of base “a” gives the product of powers raised to base “a” such as

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

**a**where a is a non zero integer and m, n are integers.

^{mn}**Example**

Express 16^{4} as a power raised to base 2?

**Solution:**

We have 2*2*2*2 = 2^{4}

Therefore (2^{4})^{4} = 2^{16}

### Product to a Power

According to this rule, for two or more different bases and the same power then

**a ^{n}. b^{n} = (ab)^{n}** where a is a non zero term and n is an integer.

**Example**

Simplify and Write the Exponential Form of 1/16*5^{-4}?

**Solution:**

We can write 1/16 as 2^{-4}

= 2^{-4}*5^{-4}

= (2*5)^{-4}

= (10)^{-4}

### Quotient to a Power

According to this law, a fraction of two different bases having the same power is given as

**a ^{n}/b^{n} = (a/b)^{n}** where a, b are non zero terms and n is an integer.

**Example**

Simplify the Expression and find the value as 12^{3}/4^{3}?

**Solution:**

Given Expression is 12^{3}/4^{3}

= (12/4)^{3}

= (3)^{3}

= 27

### Zero Power

As per the rule, Any integer raised to the power of 0 is 1 such that a^{0} = 1 and a is a non-zero term.

**Example**

What is the value of 4^{0} + 11^{0} + 3^{0} + 17^{0} – 3^{1}?

**Solution:**

Given 4^{0} + 11^{0} + 3^{0} + 17^{0} – 3^{1}

Any number raised to the power 0 is 1.

= 1+1+1+1-3

= 4-3

= 1