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Lesson 3: Quotient of Powers Property — Practice Questions

  1. 1. Simplify the expression $\frac{y^9}{y^3}$. The result is $y$ raised to the power of ___.

  2. 2. Which expression is equivalent to the quotient $\frac{x^8}{x^2}$?

    • A. $x^4$
    • B. $x^6$
    • C. $x^{10}$
    • D. $x^{16}$
  3. 3. When the expression $\frac{k^4}{k^{11}}$ is simplified to the form $k^n$, the value of $n$ is ___.

  4. 4. Which of the following correctly simplifies the expression $\frac{p^2}{p^7}$?

    • A. $p^5$
    • B. $p^9$
    • C. $p^{-5}$
    • D. $p^{-9}$
  5. 5. The population of a major city is about $10^7$, while a small town has about $10^4$ people. The city's population is ___ times larger than the town's population.

  6. 6. The distance from Earth to Star X is $10^{18}$ meters, while the distance to Star Y is $10^{15}$ meters. How many times farther away is Star X compared to Star Y?

    • A. $10^3$
    • B. $10^{33}$
    • C. $10^{1.2}$
    • D. 3
  7. 7. A computer's hard drive has $2^{33}$ bytes of memory. A large video file takes up $2^{29}$ bytes. The total memory is ___ times larger than the video file.

  8. 8. A powerful supercomputer can perform $10^{15}$ calculations per second. A standard laptop can perform $10^{11}$ calculations per second. How many times faster is the supercomputer?

    • A. $10^4$
    • B. $10^{26}$
    • C. 4
    • D. $10^{1.36}$
  9. 9. A digital library contains $2^{50}$ bytes of data. If the average book is $2^{20}$ bytes, the library can hold ___ times the data of a single average book.