Integer exponent rules Transitional Reasoning Download PDF

Questions

1. 1.

   A high-throughput DNA sequencing machine generates a total data volume of $\left(12^4 \cdot 6^{-2}\right)^2$ megabytes during an automated diagnostic run. The output data is divided into identical read-out files, each occupying $8^3 \cdot 3^2$ megabytes of storage. How many complete read-out files are generated during this sequencing run?

   • A) 24
   • B) 36
   • C) 72
   • D) 144
2. 2.

   A materials science laboratory synthesizes a sample of an experimental composite alloy. The sample has a total mass of $\left(24^3 \cdot 3^{-3}\right)^2$ milligrams and occupies a volume of $16^4 \cdot 4^{-1}$ cubic millimeters. What is the density of the alloy sample in milligrams per cubic millimeter, expressed as a single power of 2?

   • A) $2^4$
   • B) $2^6$
   • C) $2^2$
   • D) $2^{-4}$
3. 3.

   An environmental research laboratory measures air quality across an industrial zone using automated sensors. A sensor records an initial particle concentration of $\left(5^{-3}\right)^2$ grams per cubic meter. Over an observation period, this concentration is multiplied by $2^{-6}$ due to filtration, and then diluted such that the resulting value is divided by $10^{-9}$. What is the simplified value of the final concentration in grams per cubic meter, expressed as a single power of 10?

   • A) $10^3$
   • B) $10^{-15}$
   • C) $10^{-3}$
   • D) $10^{15}$
4. 4.

   A digital archiving server divides a master data file of size $2^{18}$ bytes into $4^3$ equal packets. During transmission, an optimization protocol compresses each packet to $\left(2^{-2}\right)^2$ of its uncompressed size. What is the final size of each compressed packet in bytes, expressed as a power of 2?

   • A) $2^8$
   • B) $2^{10}$
   • C) $2^{14}$
   • D) $2^{16}$