Exponential Arithmetic

Before coming to this blog, I assume you have learned the fundamentals of basic arithmetic (addition, subtraction, multiplication, and division of numbers). $4+4=8$, $10∗6=60$, $7−3=4$, and $\frac{12}{2}=6$ should all be very comfortable to calculate. When it’s 11:37 and you calculate there are 23 minutes until lunch at noon you have used arithmetic. When someone hands you a five dollar bill for a \$4.75 churro, you hand them \$0.25 back and have done arithmetic.

Less common in daily experience is exponential arithmetic. We can write two times two as $2*2$, but we can also write it using exponential notation, $2^2$. This is called squaring a number. In this example, "two squared".

We can square any number we desire: $3*3 = 3^2$, $6*6 = 6^2$

When we multiply three copies of a number, it is called cubing: $3*3*3 = 3^3$, $6*6*6= 6^2$

In general, we can multiply as many copies of a number that we want, this is called exponentiation.