Negative Numbers and Exponential

The birth of negative numbers
In the early days of algebra, negative numbers
weren’t an accepted entity. Mathematicians had
a hard time explaining exactly what the numbers
illustrated; it was too tough to come up with concrete
examples. One of the first mathematicians
to accept negative numbers was Fibonacci, an
Italian mathematician. When he was working on
a financial problem, he saw that he needed what
amounted to a negative number to finish the
problem. He described it as a loss and proclaimed,
“I have shown this to be insoluble
unless it is conceded that the man had a debt.”

Expounding on Exponential Rules
Several hundred years ago, mathematicians introduced powers of variables
and numbers called exponents. The use of exponents wasn’t immediately
popular, however. Scholars around the world had to be convinced; eventually,
the quick, slick notation of exponents won over, and we benefit from the
use today. Instead of writing xxxxxxxx, you use the exponent 8 by writing x8.
This form is easier to read and much quicker.
The expression an is an exponential expression with a base of a and an exponent
of n. The n tells you how many times you multiply the a times itself.
You use radicals to show roots. When you see sqrt(16), you know that you’re looking
for the number that multiplies itself to give you 16. The answer? Four, of
course. If you put a small superscript in front of the radical, you denote a cube
root, a fourth root, and so on. For instance, 4th root of 81 = 3, because the number 3
multiplied by itself four times is 81. You can also replace radicals with fractional
exponents — terms that make them easier to combine. This system of
exponents is very systematic and workable — thanks to the mathematicians
that came before us.