7th Class Mathematics Exponents and Power Question Bank

done Exponents and Power Total Questions - 40

• question_answer1)
  \[{{5}^{3}}+{{5}^{3}}+{{5}^{3}}+{{5}^{3}}+{{5}^{3}}\]is equal to
  A)
  \[{{5}^{4}}\]                           done clear
  B)
  \[{{55555}^{3}}\] done clear
  C)
  \[{{5}^{5}}\]                                       done clear
  D)
   None of these done clear
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• question_answer2)
  \[{{\left\{ {{3}^{-2}}+{{\left( \frac{3}{2} \right)}^{-2}} \right\}}^{-1}}=?\]
  A)
  \[{}^{81}/{}_{4}\]                               done clear
  B)
   \[{}^{5}/{}_{9}\] done clear
  C)
  \[\frac{9}{5}\]                           done clear
  D)
  \[\frac{4}{81}\] done clear
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• question_answer3)
  What is the value of\[\left( 1{}^\circ \times 2{}^\circ  \right)\times {{5}^{2}}?\]
  A)
   25          done clear
  B)
   0             done clear
  C)
   \[-25\]              done clear
  D)
   1 done clear
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• question_answer4)
  \[{{\left( \frac{5}{7} \right)}^{5}}\]can be written as
  A)
   \[{{\left( \frac{7}{5} \right)}^{5}}\]                               done clear
  B)
  \[{{\left( 57 \right)}^{6}}\] done clear
  C)
  \[\frac{{{5}^{5}}}{{{7}^{5}}}\]               done clear
  D)
  \[{{\left( {{5}^{5}} \right)}^{7}}\] done clear
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• question_answer5)
  Which of the following values are equal?

  (i)\[{{1}^{3}}\]	(ii)\[4{}^\circ \]
  (iii)\[{{0}^{4}}\]	(iv)\[{{3}^{1}}\]

  A)
   (i) and (ii)      done clear
  B)
   (ii) and (iii)      done clear
  C)
   (i) and (iii)                     done clear
  D)
   (i) and (iv) done clear
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• question_answer6)
  What is the sum of the powers of the prime factors in\[72\times 1927\]?
  A)
   5                                 done clear
  B)
   7             done clear
  C)
   8                                 done clear
  D)
   12 done clear
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• question_answer7)
  Express \[{{\left( -3 \right)}^{4}}\div {{n}^{4}}\]in the form\[{{\left( \frac{a}{b} \right)}^{m}}\].
  A)
  \[\frac{-24}{{{n}^{3}}}\]                                 done clear
  B)
   \[{{\left( -\frac{3}{4} \right)}^{4}}\] done clear
  C)
   \[\frac{{{\left( -2 \right)}^{4}}}{{{n}^{4}}}\]              done clear
  D)
  \[\left( \frac{-3}{n} \right)\times \left( \frac{-3}{n} \right)\] done clear
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• question_answer8)
  Which of the following is the smallest number?
  A)
  \[{{1}^{5}}\]                           done clear
  B)
  \[{{(-10)}^{1}}\] done clear
  C)
  \[{{(-1)}^{4}}\]                                    done clear
  D)
  \[{{(-1)}^{3}}\] done clear
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• question_answer9)
  Express\[\underline{a\times a\times a}\]\[\times \]\[\underline{c\times c\times c\times c}\]\[\times \]\[b\times b\]in exponential form.
  A)
  \[{{a}^{3}}{{c}^{3}}{{b}^{3}}\]                             done clear
  B)
  \[{{a}^{3}}{{c}^{3}}b\] done clear
  C)
  \[{{a}^{3}}{{c}^{3}}b\]                                done clear
  D)
  \[{{a}^{3}}{{c}^{4}}{{b}^{2}}\] done clear
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• question_answer10)
  Which of the following statements is correct?
  A)
  \[{{({{2}^{3}})}^{2}}\] and \[{{({{3}^{2}})}^{4}}\] are not the same done clear
  B)
   \[{{({{2}^{3}})}^{2}}\] and \[{{({{3}^{4}})}^{2}}\] are the same done clear
  C)
   \[{{({{6}^{49}})}^{2}}={{6}^{492}}\]                       done clear
  D)
  \[{{({{8}^{7}})}^{3}}={{8}^{10}}\] done clear
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• question_answer11)
  What is the value of\[{{2}^{4}}\times {{5}^{3}}\]
  A)
   2453                            done clear
  B)
   2000          done clear
  C)
   11200             done clear
  D)
   10000000 done clear
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• question_answer12)
  Find the value of\[{{2}^{0}}+{{3}^{0}}+{{4}^{0}}+{{5}^{0}}+{{6}^{0}}+{{7}^{1}}\]
  A)
   12        done clear
  B)
   234           done clear
  C)
   1                                 done clear
  D)
   24 done clear
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• question_answer13)
  What is the result of\[\frac{{{2}^{1}}\times {{3}^{2}}\times {{3}^{3}}}{{{1}^{2}}\times {{4}^{2}}}\]?
  A)
  \[\frac{243}{8}\]            done clear
  B)
   42 done clear
  C)
  \[\frac{46}{16}\]                                    done clear
  D)
   48 done clear
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• question_answer14)
  Express \[\frac{729\times 64}{270}\] as a product of prime factors in exponential form.
  A)
   \[\frac{{{2}^{6}}\times {{3}^{4}}}{27}\]                   done clear
  B)
  \[\frac{{{2}^{5}}\times {{3}^{3}}}{5}\] done clear
  C)
  \[\frac{{{2}^{5}}\times {{3}^{3}}}{{{5}^{3}}}\]                  done clear
  D)
  \[\frac{{{2}^{6}}\times {{3}^{2}}}{{{5}^{2}}}\] done clear
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• question_answer15)
  The value \[\frac{{{\left( -\frac{1}{2} \right)}^{5}}}{{{\left( -\frac{1}{2} \right)}^{4}}}\div \frac{\left( -\frac{1}{8} \right)}{\left( -\frac{1}{4} \right)}\] is
  A)
   1                                 done clear
  B)
   2            done clear
  C)
   3                                 done clear
  D)
  \[-1\] done clear
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• question_answer16)
  If \[\frac{x}{y}={{\left( \frac{6}{7} \right)}^{3}}\div {{\left( \frac{7}{6} \right)}^{-3}},\] then the value of \[{{\left( \frac{x}{y} \right)}^{-10}}\] is
  A)
   1 done clear
  B)
   0 done clear
  C)
   \[-1\]                              done clear
  D)
   Cannot be determined done clear
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• question_answer17)
  The value \[\left( {{9}^{\frac{4}{3}}}\div {{81}^{\frac{2}{3}}} \right)\times {{3}^{\frac{3}{2}}}\]is.......
  A)
   36                                done clear
  B)
   32    done clear
  C)
   \[{{3}^{\frac{27}{6}}}\]                     done clear
  D)
   None of these done clear
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• question_answer18)
  The value of\[{{\left( \frac{8}{125} \right)}^{\frac{-4}{3}}}\]
  A)
  \[\frac{625}{16}\]                      done clear
  B)
  \[\frac{125}{16}\] done clear
  C)
  \[\frac{16}{25}\]                                    done clear
  D)
  \[\frac{-625}{16}\] done clear
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• question_answer19)
  Cube of \[\left( -\frac{1}{9} \right)\] is............
  A)
  \[\left( \frac{-1}{729} \right)\]                   done clear
  B)
  \[\frac{1}{963}\] done clear
  C)
  \[\frac{1}{850}\]                                    done clear
  D)
  \[\left( \frac{1}{729} \right)\] done clear
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• question_answer20)
  If \[{{8}^{x-1}}={{2}^{x+3}},\]then \[x\] is
  A)
   2                                 done clear
  B)
   1             done clear
  C)
   0                                 done clear
  D)
   3 done clear
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• question_answer21)
  If\[\sqrt{{{3}^{x}}}=243,\] then\[x=\]?
  A)
   2                                 done clear
  B)
   4             done clear
  C)
   6                                 done clear
  D)
   10 done clear
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• question_answer22)
  If \[{{3}^{x}}=300\], then the value of \[{{3}^{x-2}}\] is
  A)
  \[\frac{200}{11}\]                      done clear
  B)
  \[\frac{300}{50}\] done clear
  C)
  \[\frac{100}{3}\]           done clear
  D)
  \[\frac{300}{2}\] done clear
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• question_answer23)
  If \[x={{y}^{3}},\]which expression is equal to\[{{y}^{1/2}}\]
  A)
  \[{{x}^{1/6}}\]        done clear
  B)
  \[{{x}^{6}}\] done clear
  C)
  \[{{x}^{1/12}}\]                      done clear
  D)
  \[{{x}^{-1/12}}\] done clear
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• question_answer24)
  Find the numerical value of\[{{\left( 4096 \right)}^{\frac{-1}{4}}}\].
  A)
   16                                done clear
  B)
   8            done clear
  C)
   4                                 done clear
  D)
  \[\frac{1}{8}\] done clear
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• question_answer25)
  Simplify\[\frac{{{\left( 9{{m}^{2}} \right)}^{1/3}}}{{{6}^{4}}}\times \frac{{{\left( 4{{n}^{2}} \right)}^{1/3}}}{5m}\].
  A)
  \[\frac{1}{5}{{\left[ \frac{{{n}^{2}}}{m{{6}^{10}}} \right]}^{1/3}}\] done clear
  B)
  \[\frac{1}{5}{{\left[ \frac{n}{{{m}^{2}}{{6}^{10}}} \right]}^{1/3}}\] done clear
  C)
  \[\frac{1}{5}{{\left[ \frac{{{n}^{2}}}{m{{6}^{-10}}} \right]}^{1/3}}\]                        done clear
  D)
  \[\frac{1}{5}{{\left[ \frac{{{n}^{2}}}{m{{6}^{10}}} \right]}^{2/3}}\] done clear
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• question_answer26)
  Simplify and leave the answer in exponent form\[{{\left( \frac{3}{5} \right)}^{-30}}\times {{\left( \frac{5}{3} \right)}^{-30}}\].
  A)
   \[\frac{3}{5}\]                          done clear
  B)
  \[{{1}^{1}}\] done clear
  C)
  \[{{\left( \frac{3}{5} \right)}^{-60}}\]                 done clear
  D)
  \[{{\left( \frac{5}{3} \right)}^{-60}}\] done clear
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• question_answer27)
  Find the numerical value of\[{{16}^{0.75}}\].
  A)
   8                                 done clear
  B)
   32             done clear
  C)
  \[{{2}^{-3}}\]          done clear
  D)
  \[{{4}^{-3}}\] done clear
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• question_answer28)
  Simplify\[\frac{{{\left( {{a}^{-n}} \right)}^{m}}\times {{a}^{-2m}}}{{{a}^{mn}}\times {{a}^{2m}}}\]
  A)
   \[100\,{{a}^{\frac{25}{4}}}\]              done clear
  B)
   \[\frac{1}{100{{a}^{\frac{21}{4}}}}\] done clear
  C)
  \[20{{a}^{\frac{-21}{4}}}\]      done clear
  D)
   \[20{{a}^{\frac{21}{4}}}\] done clear
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• question_answer29)
  Simplify\[\frac{{{\left( 9{{a}^{2}} \right)}^{1/2}}\times {{\left( 25{{a}^{4}} \right)}^{\frac{-1}{2}}}}{5{{a}^{1/2}}\times 3{{a}^{1/2}}\times 4{{a}^{9/4}}}\]
  A)
   \[100\,{{a}^{\frac{25}{4}}}\]              done clear
  B)
   \[\frac{1}{100{{a}^{\frac{21}{4}}}}\] done clear
  C)
  \[20{{a}^{\frac{-21}{4}}}\]                  done clear
  D)
   \[20\,{{a}^{\frac{21}{4}}}\] done clear
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• question_answer30)
  Express \[{{6}^{2}}\times \] \[{{7}^{-4}}\times \]\[{{({{8}^{-2}})}^{2}}\times \]\[{{6}^{3}}\times \]\[{{({{7}^{2}})}^{2}}{{8}^{4}}\] in the simplest exponential form.
  A)
  \[{{6}^{5}}{{7}^{2}}\]                      done clear
  B)
  \[{{6}^{5}}\] done clear
  C)
  \[{{6}^{-5}}{{7}^{2}}\]                                 done clear
  D)
  \[{{6}^{-5}}{{7}^{2}}\] done clear
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• question_answer31)
  Solve \[{{81}^{2x}}={{\left( 729 \right)}^{2}}\]
  A)
  \[x=\frac{3}{4}\]                       done clear
  B)
  \[x=\frac{2}{3}\] done clear
  C)
  \[x=\frac{5}{6}\]                       done clear
  D)
  \[x=\frac{3}{2}\] done clear
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• question_answer32)
  Which of the following has the same value of \[{{3}^{6}}\times {{({{3}^{-2}})}^{2}}\times {{({{2}^{3}})}^{2}}\times {{({{2}^{-2}})}^{3}}\]
  A)
  \[9{}^\circ \]                             done clear
  B)
  \[9\] done clear
  C)
  \[{{9}^{2}}\]                           done clear
  D)
  \[{{9}^{3}}\] done clear
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• question_answer33)
  The value of x so that \[{{\left( \frac{2}{7} \right)}^{4}}.{{\left( \frac{2}{7} \right)}^{3}}={{\left( \frac{2}{7} \right)}^{4x-1}}\]is
  A)
   \[1\]                             done clear
  B)
   2 done clear
  C)
   3                                 done clear
  D)
   4 done clear
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• question_answer34)
  Avogadro number is written as\[602,\]\[000,\]\[000,\]\[000,\]\[000,\]\[000,\]\[000,\]\[000\]. Express this number in standard form.
  A)
  \[6.02\times {{10}^{23}}\]    done clear
  B)
  \[6.02\times {{10}^{21}}\]      done clear
  C)
  \[602.0\times {{10}^{21}}\]                  done clear
  D)
  \[0.602\times {{10}^{23}}\] done clear
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• question_answer35)
  What is the simplified form of\[{{\left( -6xy \right)}^{6}}\div {{\left( -6xy \right)}^{2}}\]?
  A)
  \[{{\left( -6xy \right)}^{6}}\]                  done clear
  B)
  \[{{\left( -6xy \right)}^{8}}\]        done clear
  C)
  \[\left( -6xy \right)\]                      done clear
  D)
  \[{{\left( -6xy \right)}^{4}}\] done clear
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• question_answer36)
  A number in standard form in written as\[6.6\times {{10}^{6}}.\] It can also be written as:
  A)
   6666666                       done clear
  B)
   66000 done clear
  C)
   6600000000                  done clear
  D)
   6600000 done clear
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• question_answer37)
  The speed of light is\[300,000,000\,\,m{{s}^{-1}}\]. Express it in standard form.
  A)
  \[3.0\times {{10}^{8}}m{{s}^{-1}}\]   done clear
  B)
  \[3.0\times {{10}^{10}}m{{s}^{-1}}\] done clear
  C)
  \[3.0\times {{10}^{6}}m{{s}^{-1}}\]               done clear
  D)
  \[3.0\times {{10}^{6}}m{{s}^{-1}}\] done clear
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• question_answer38)
  Which is greater \[{{4}^{3}}\]or\[{{3}^{4}}\]?
  A)
   Both are equal done clear
  B)
  \[{{4}^{3}}\] done clear
  C)
  \[{{3}^{4}}\] done clear
  D)
   Cannot be determined done clear
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• question_answer39)
  Solve\[{{\left( {{4}^{5}} \right)}^{x}}={{\left( {{4}^{4}} \right)}^{x}}\div {{4}^{2}}\]
  A)
  \[x=4\]                          done clear
  B)
  \[x=-2\] done clear
  C)
  \[x=-3\]            done clear
  D)
  \[x=2\] done clear
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• question_answer40)
  The value of \[\frac{{{x}^{-4}}\times {{y}^{-6}}}{{{x}^{-16}}\times {{y}^{-7}}}\]
  A)
  \[{{x}^{-1}}\times {{y}^{-1}}\]                      done clear
  B)
  \[{{x}^{-1}}\text{ }{{y}^{-1}}\] done clear
  C)
  \[\frac{1}{{{x}^{12}}y}\]                                done clear
  D)
  \[{{x}^{12}}y\] done clear
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