This problem is going to reveal the first name of the offender.

Question

Simplify the expression:
(6^4⋅6^9/6^3)3
If the simplified expression is

6^16
, the first name of the culprit is Mandy.
If the simplified expression is

6^18
, the first name of the culprit is Lila.
If the simplified expression is

6^30
, the first name of the culprit is Ervin.
If the simplified expression is

6^33
, the first name of the culprit is Dean.

Answer 1

Seems to me like it would be 6^30.

Reduce the division first, going by the rule that dividing numbers means subtracting exponents IF the base is the same.

6^9/6^3 = 6^6

6^4 * 6^6 = 6^10.

6^10 cubed = 6^30.

Answer 2

(6^4*6^9/6^3)^3 = (6^13/6^3)^33 = (6^10)^3 = 6^30.