Exponents Basics

By the Rules of Exponents ,

$a^{b+c} = a^{b} \cdot a^{c}.$

An intuitive way to remember this is that if you want to multiply $b+c$ copies of $a,$ you can multiply $b$ copies and multiply $c$ copies, and then multiply those results together. E.g., $2^{3+2} = 2\cdot 2 \cdot 2 \cdot 2 \cdot 2 = (2\cdot 2 \cdot 2)(2\cdot 2) = 2^{3} \cdot 2^{2}.$

The rules of exponents state that if two indices with same base are multiplied, the powers are added. So, $a^{b + c} = \color{#69047E}{\boxed{a^ba^c}}$ .

a^n = a* a* a* a....n times

a^b+c = a* a* a....b+c times

    = a* a* a....b times* a*a...c times 

    =a^b * a^c

a^b+c=a^b.a^c. this is the simplest rule in logarithm . if the power of a base can be written by a + sign then we can separate them by multiplying them having the same base .

a^m x a^n = a^m+n So a^b+c = a^b x a^c