This problem is going to reveal the first name of the offender.
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.
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.
(6^4*6^9/6^3)^3 = (6^13/6^3)^33 = (6^10)^3 = 6^30.
To solve the problem and determine the culprit's first name, we need to simplify the given expression. Let's break down the process step by step.
The expression we're given is:
(6^4 * 6^9 / 6^3)^3
To simplify this expression, we can start by simplifying the exponents separately.
Using the exponent rule of multiplication, we add the exponents when the bases are the same. And when we divide the same bases, we subtract the exponents.
Let's simplify the exponents:
6^4 * 6^9 = 6^(4 + 9) = 6^13
Then, 6^13 / 6^3 = 6^(13 - 3) = 6^10
Now, we can substitute the simplified expression back into the original equation:
(6^10)^3 = 6^(10 * 3) = 6^30
Therefore, if the simplified expression is 6^30, the first name of the culprit is Ervin.