Laws in physics are formulated in abstract form, that is, establishing relationships between variables that can assume any value. Algebra gives us the rules to manipulate these expressions and obtain new expressions as necessary.

(ID 491)

In case two variables a and b are equal, the sign = is used to indicate this fact:

(ID 3305)

$c = a+b$

(ID 3301)

$c=a-b$

(ID 3302)

$a+b=b+a$

(ID 3304)

$b+(-b)=0$

(ID 3303)

$c=a*b$

(ID 3306)

$a*b=b*a$

(ID 3312)

$b*(b^{-1})=1$

(ID 3307)

$c=\displaystyle\frac{a}{b}$

(ID 3308)

$c=a^b$

(ID 3309)

$a^{b_1}a^{b_2}=a^{b_1+b_2}$

(ID 3311)

$a^{b+(-b)}=a^{b-b}=a^0=1$

(ID 3310)

$a^0=1$

(ID 3313)