# Laws of Exponents

There are three types of properties to study the exponents and here is the list of exponential function rules with proofs in algebraic form for beginners.

01

### Product Rules

There are two types of fundamental product laws of exponents.

$(1)\,\,\,\,\,\,$ $\large b^{\displaystyle m} \times b^{\displaystyle n} = b^{\displaystyle \,m+n}$

$(2)\,\,\,\,\,\,$ $\large b^{\displaystyle m} \times c^{\displaystyle m} = (b \times c)^{\displaystyle m}$

02

### Quotient Rules

There are two division rules of indices.

$(1)\,\,\,\,\,\,$ $\large \dfrac{b^{\displaystyle m}}{b^{\displaystyle n}} \,=\, b^{\displaystyle m-n}$

$(2)\,\,\,\,\,\,$ $\large \dfrac{b^{\displaystyle m}}{c^{\displaystyle m}} \,=\, {\Bigg(\dfrac{b}{c}\Bigg)}^{\displaystyle m}$

03

### Power Rules

There are six exponential power rules.

$(1)\,\,\,\,\,\,$ $\large {(b^m)}^n \,=\, b^{mn}$

$(2)\,\,\,\,\,\,$ $\large b^{-m} \,=\, \dfrac{1}{b^m}$

$(3)\,\,\,\,\,\,$ $\large b^{\frac{1}{n}} \,=\, \sqrt[\displaystyle n]{b}$

$(4)\,\,\,\,\,\,$ $\large b^{\frac{m}{n}} \,=\, \sqrt[\displaystyle n]{b^m}$

$(5)\,\,\,\,\,\,$ $\large b^0 \,=\, 1$

$(6)\,\,\,\,\,\,$ $\large b^1 \,=\, b$