Anumber to the 11th power divided by the same number to the 8th power equals 216. what is the number?

Let "a number" be signified by x.
"A number" to the 11th power,
x^11

divided by "the same number" to the 8th power,
x^11 / x^8

equals 216,
x^11 / x^8 = 216

Apply your exponent rule, division to subtraction,
x^(11-8) = 216
x^3 = 216

"the number" is being raised to the third power.
To isolate our number, x, we'll apply the inverse of raising to a power:
Taking a third root (or applying a 1/3 power).



and simplify,

x= 6