Name of numbers in "to the power of" and factorial calculations

Question

In $4*5=20$ , $4$ and $5$ are multiplicands and $20$ is the product. What are the names / labels of the numbers in the following expressions?

$2^3=8$

$4!=24$

Answer 1

For $b^a$, $b$ is usually called the base, $a$ is called the exponent and the result $b^a$ is called the $a$-th power of $b$. So in your case, the base is $2$, the exponent is $3$ and $8$ is the $3^{rd}$ power of $2$.

I'm not aware of any specific name for the operand of $n!$. The result is called the factorial of $n$, though.