Geoffrey is evaluating the expression (-3) ^6 (2^6) / (-3) ^5 (2^2) as shown below.

48.

Step-by-step explanation:

First you multiply the number by itself as many times as the number of the exponent is. In this case you multiply - 3 to itself 6 times which makes - 729, 2 to the 6th power is 64, - 3 to the 5th power is - 243, and 2 to the 2nd power is 4. Then you multiply - 729 by 64 which makes - 46656 and multiply - 243 by 4 which makes - 972, and then divide - 972 from - 46656 which makes 48.