Random Puzzles 

Workings

Hint
The word begins with the letter A.

Answer
Arm.

Double-Checking
swarm army alarm farm warm

Workings

Hint
Think of squares and cubes.

Answer
512.

Each term alternates between a square and a cube, 8 3 = 512.

Workings

Hint
One possibility answer might be associated with an apiary.

Answer
Common words: beekeeper, beekeepers, beekeeping, freebee, freebees, freewheel, freewheeled, freewheeling, freewheels, peewee, peewees, reengineer, reengineered, reengineering, reengineers, squeegee, squeegeed, squeegeeing, squeegees, teepee, teepees.

All words: beebee, beebees, beekeeper, beekeepers, beekeeping, beekeepings, beetleweed, beetleweeds, cheekteeth, deepfreeze, deepfreezes, deepfreezing, deerweed, deerweeds, freebee, freebees, freesheet, freesheets, freewheel, freewheeled, freewheeler, freewheelers, freewheeling, freewheelingly, freewheelings, freewheels, geechee, geechees, greegree, greegrees, greenkeeper, greenkeepers, greenleek, greenskeeper, greenskeepers, greenweed, greenweeds, leechee, leechees, peebeen, peebeens, peesweep, peesweeps, peetweet, peetweets, peewee, peewees, preengineered, reengineer, reengineered, reengineering, reengineers, sleeveen, sleeveens, sneezeweed, sneezeweeds, squeegee, squeegeed, squeegeeing, squeegees, streetkeeper, streetkeepers, teepee, teepees, teetee, treecreeper, treecreepers, tweedledee, tweedledeed, tweedledeeing, tweedledees, veepee, veepees, weewee, weeweed, weeweeing, weewees.

Workings

Hint
There are at least 4 answers that fit the question.

Answer
A hole or a vacuum, or perhaps a set of scales, or maybe a shadow.