(6561)(1/2) + (6561)(1/4) + (6561)(1/8)

For a positive base expressed as a power of a smaller number, a fractional exponent b(k/n) equals the n-th root of bk; equivalently, (ak)(1/n) = a(k/n). Rewriting a large number as a power of a prime turns tricky roots into simple exponent division, avoiding messy root calculations.

Here 6561 = 38, so each term becomes:

1. 6561(1/2) = (38)(1/2) = 3(8/2) = 34 = 81

2. 6561(1/4) = (38)(1/4) = 3(8/4) = 32 = 9

3. 6561(1/8) = (38)(1/8) = 3(8/8) = 31 = 3

4. Adding the three values: 81 + 9 + 3 = 93

Cross-check: since 34 = 81, squaring gives 812 = 6561, confirming 38 = 6561 and that 6561(1/2) = 81. The sum of all three terms is 93.