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3.11: Proficiency Exam

  • Page ID
    58494
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    Proficiency Exam

    Simplify the expressions for the following problems.

    Exercise \(\PageIndex{1}\)

    \(-\{-[(-6)]\}\)

    Answer

    \(-6\)

    Exercise \(\PageIndex{2}\)

    \(-|-15|\)

    Answer

    \(-15\)

    Exercise \(\PageIndex{3}\)

    \(-[|-12|-10]^2\)

    Answer

    \(-4\)

    Exercise \(\PageIndex{4}\)

    \(-5(-6)+4(-8)-|-5|\)

    Answer

    \(-7\)

    Exercise \(\PageIndex{5}\)

    \(\dfrac{3(-8)-(-2)(-4-5)}{(-2)(-3)}\)

    Answer

    \(-7\)

    Exercise \(\PageIndex{6}\)

    \(-|7|-(2)^2+(-2)^2\)

    Answer

    \(-7\)

    Exercise \(\PageIndex{7}\)

    \(\dfrac{-6(2)(-2)}{-(-5-3)}\)

    Answer

    \(3\)

    Exercise \(\PageIndex{8}\)

    \(\dfrac{-2\{[(-2-3)][-2]\}}{-3(4-2)}\)

    Answer

    \(5\)

    Exercise \(\PageIndex{9}\)

    If \(z = \dfrac{x-u}{s}\), \(z\) is \(x = 14, u = 20\), and \(s = 2\).

    Answer

    \(-3\)

    When simplifying the terms for the following problems, write each so that only positive exponents appear.

    Exercise \(\PageIndex{10}\)

    \(\dfrac{1}{-(-5)^{-3}}\)

    Answer

    \(125\)

    Exercise \(\PageIndex{11}\)

    \(\dfrac{5x^3y^{-2}}{x^{-4}}\)

    Answer

    \(\dfrac{5x^3z^4}{y^2}\)

    Exercise \(\PageIndex{12}\)

    \(2^{-2}m^6(n-4)^{-3}\)

    Answer

    \(\dfrac{m^6}{4(n-4)^3}\)

    Exercise \(\PageIndex{13}\)

    \(4a^{-6}(2a^{-5})\)

    Answer

    \(\dfrac{8}{a^{11}}\)

    Exercise \(\PageIndex{14}\)

    \(\dfrac{6^{-1}x^3y^{-5}z^{-3}}{y^{-5}}\)

    Answer

    \(\dfrac{1}{6}\)

    Exercise \(\PageIndex{15}\)

    \(\dfrac{(k-6)^2(k-6)^{-4}}{(k-6)^3}\)

    Answer

    \(\dfrac{1}{(k-6)^5}\)

    Exercise \(\PageIndex{16}\)

    \(\dfrac{(y+1)^3(y-3)^4}{(y+1)^5(y-3)^{-8}}\)

    Answer

    \(\dfrac{(y-3)^{12}}{(y+1)^2}\)

    Exercise \(\PageIndex{17}\)

    \(\dfrac{(3^{-6})(3^2)(3^{-10})}{(3^{-5})(3^{-9})}\)

    Answer

    \(1\)

    Exercise \(\PageIndex{18}\)

    \((a^4)^{-3}\)

    Answer

    \(\dfrac{1}{a^{12}}\)

    Exercise \(\PageIndex{19}\)

    \([\dfrac{r^6s^{-2}}{m^{-5}n^4}]^{-4}\)

    Answer

    \(\dfrac{n^{16}s^8}{m^{20}r^{24}}\)

    Exercise \(\PageIndex{20}\)

    \((c^0)^{-2}, c \not = 0\)

    Answer

    \(1\)

    Exercise \(\PageIndex{21}\)

    Write 0.000271 using scientific notation.

    Answer

    \(2.71 \times 10^{-4}\)

    Exercise \(\PageIndex{22}\)

    Write \(8.90 \times 10^5\) in standard form.

    Answer

    890,000

    Exercise \(\PageIndex{23}\)

    Find the value of \((3 \times 10^5)(2 \times 10^{2})\).

    Answer

    6000

    Exercise \(\PageIndex{24}\)

    Find the value of \((4 \times 10^{-16})^2\)

    Answer

    \(1.6 \times 10^{-31}\)

    Exercise \(\PageIndex{25}\)

    If \(k\) is a negative integer, is \(-k\) a positive or negative integer?

    Answer

    a positive integer


    This page titled 3.11: Proficiency Exam is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Denny Burzynski & Wade Ellis, Jr. (OpenStax CNX) .

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