Whole-number exponents Transitional Reasoning Practice

Questions

1. 1.

   A chemist combines liquid samples from three separate containers into an empty glass flask that has a maximum capacity of $6^3\text{ mL}$. The three containers hold $10^2\text{ mL}$, $3^4\text{ mL}$, and $2^7\text{ mL}$ of solution, respectively. If all the liquid from the three containers is poured into the flask, how many milliliters of solution will overflow?

   • A) 29 mL
   • B) 76 mL
   • C) 93 mL
   • D) 103 mL
2. 2.

   A logistics warehouse uses automated sorting bins that process packages according to specific programmed power rules. On a certain morning, Bin P receives $7^2 + 2^5$ packages, while Bin Q receives $3^4 - 4^2$ packages. To balance the workload evenly across both stations, a technician transfers packages from the fuller bin to the other so that both bins contain the exact same number of packages. How many packages must be transferred from Bin P to Bin Q?

   • A) 8
   • B) 16
   • C) 24
   • D) 10
3. 3.

   A landscaping crew uses identical 1-meter square stone pavers to construct two community plazas. Plaza X is designed as a single square with a side length of $2^3\text{ meters}$. Plaza Y consists of $5^2$ individual 1-meter square plots plus an additional rectangular walkway requiring $2^4$ pavers. How many more 1-meter square pavers are needed to complete Plaza X than Plaza Y in total?

   • A) 18
   • B) 39
   • C) 23
   • D) 31
4. 4.

   A digital storage platform organizes items using hierarchical branching. User X creates 3 primary folders, where each primary folder holds 3 secondary folders, each secondary folder holds 3 project folders, and each project folder contains 3 documents. User Y creates 4 archive folders, where each archive folder holds 4 subfolders, and each subfolder contains 4 reports. How many more documents does User X have than the number of reports User Y has?

   • A) 0
   • B) 11
   • C) 37
   • D) 17

Answers and step-by-step solutions appear after you finish the test.