Math Doubts

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.

Product Rules

There are two types of fundamental product laws of exponents.

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

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

Quotient Rules

There are two division rules of indices.

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

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

Power Rules

There are six exponential power rules.

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

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

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

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

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

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

Math Doubts
Math Doubts is a free math tutor for helping students to learn mathematics online from basics to advanced scientific level for teachers to improve their teaching skill and for researchers to share their research projects. Know more
Follow us on Social Media
Math Problems

Learn how to solve easy to difficult mathematics problems of all topics in various methods with step by step process and also maths questions for practising.

Learn more