**Laws of
Exponents**

The **laws of exponents** refer to a set of **rules**
for **multiplying**, **dividing** and even **raising exponents to powers**
to make these operations easier.

The **product rule** is used to multiply exponents with
the same base. It states that to **multiply
two numbers** with the **same base** all you do is **add** their **exponents**.

Example: 2^{2 }· 2^{3} = 2^{5} 2^{5}=32

2^{ }· 2 · 2 · 2
· 2 = 32

*a ^{m
}*

The **quotient rule** is used to divide exponents with
the same base. It states that to **divide
two numbers** with the **same base** all you do is **subtract** their **exponents**.

Example: 10^{5 }¸ 10^{3} = 10^{2} 10^{2}=100

10^{5}=100,000

10^{3}=1,000

100,000 ¸ 1,000 = 100

*a ^{m }*

3·2=6

The

**power rule** is used to raise a number already
written as an exponent to another power.
It states that to **raise **an** exponent to a power you multiply **the**
exponents**.

Example: (3^{3})^{2
} =
3^{3} ^{ }· 3^{3} 3^{3} ^{ }· 3^{3} = 3^{6}

If you wrote
this out you would get 3^{ }· 3
· 3 · 3
· 3^{ }· 3 or 3^{6}

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

The **power of a product rule** is as follows

To find the power of a product, find the power of each factor and multiply

(ab)^{m}= a^{m}b^{m}

^{ }

And the **power of a quotient rule** is as follows

To find the value of a quotient, find the power of each number and divide.

_{}