8th Class Mental Ability Exponents and Power Question Bank

done Exponents and Powers Total Questions - 39

• question_answer1)
  Find the value of\[\sqrt[3]{343}\times \sqrt[3]{-64}.\]
  A)
   28                          done clear
  B)
  -28                         done clear
  C)
          18                          done clear
  D)
          -18                         done clear
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• question_answer2)
  Which of the following statements is false?
  A)
  \[{{(-1)}^{n}}=-1,\] if 'n' is an odd integer. done clear
  B)
   For any rational number \[a,{{a}^{o}}=1.\] done clear
  C)
   If \[4\times {{8}^{m}}={{2}^{5}}\]then m = 1. done clear
  D)
  \[{{(27)}^{\frac{1}{3}}}={{\left( \frac{1}{3} \right)}^{-1}}.\] done clear
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• question_answer3)
  If \[{{2}^{a}}+{{3}^{b}}=43\]and \[{{2}^{a+3}}-{{3}^{b+1}}=47,\]find the respective values of 'a' and 'b'.
  A)
   4, 3        done clear
  B)
          3, 4                        done clear
  C)
          16, 27                   done clear
  D)
          2, 6 done clear
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• question_answer4)
  Find the value of  \[\frac{1}{{{(216)}^{-\frac{2}{3}}}}+\frac{1}{{{(256)}^{-\frac{3}{4}}}}+\frac{1}{{{(32)}^{-\frac{1}{5}}}}.\]
  A)
   102       done clear
  B)
          105                        done clear
  C)
          107                        done clear
  D)
   109 done clear
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• question_answer5)
  Find the value of 'x', if\[{{(18)}^{3.5}}\div {{(27)}^{3.5}}\times {{6}^{3.5}}={{2}^{x}}.\]
  A)
   3.5         done clear
  B)
          4.5                         done clear
  C)
          6             done clear
  D)
          7 done clear
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• question_answer6)
  If \[{{5}^{x-1}}+{{5}^{x+1}}=3250,\] find the value of x.
  A)
   3             done clear
  B)
   4             done clear
  C)
          2             done clear
  D)
          1 done clear
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• question_answer7)
  Simplify \[\frac{{{5}^{n+2}}-{{6.5}^{n+1}}}{{{13.5}^{n}}-{{2.5}^{n+1}}}.\]
  A)
   \[\frac{-2}{3}\]                 done clear
  B)
         \[\frac{-5}{3}\]                  done clear
  C)
   \[\frac{7}{3}\]                   done clear
  D)
          \[\frac{8}{3}\] done clear
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• question_answer8)
  Find the value of \[{{(16)}^{0.16}}\times {{(16)}^{0.09}}.\]
  A)
   1                             done clear
  B)
          2                             done clear
  C)
   4                             done clear
  D)
          3 done clear
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• question_answer9)
  Find the value \[x\]in the expression \[\sqrt{{{\left( \frac{3}{5} \right)}^{1-2x}}}=4\frac{17}{27}.\]
  A)
   \[\frac{3}{2}\]                   done clear
  B)
          \[\frac{5}{2}\]                   done clear
  C)
   \[\frac{7}{2}\]                   done clear
  D)
          \[\frac{9}{2}\] done clear
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• question_answer10)
  Simplify \[{{2012}^{3}}\times {{2012}^{-3}}.\]
  A)
   2012      done clear
  B)
   1             done clear
  C)
   0                             done clear
  D)
          -1 done clear
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• question_answer11)
  If \[81\times 81\times 81\times 81=9x,\]what is the value of \['x'\,?\]
  A)
   9                             done clear
  B)
          10                          done clear
  C)
   12                          done clear
  D)
          20 done clear
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• question_answer12)
  Find the value of \[{{2012}^{o}}+{{2013}^{o}}.\]
  A)
   0                             done clear
  B)
          1                             done clear
  C)
   -1                                           done clear
  D)
   2 done clear
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• question_answer13)
  Simplify \[\frac{{{\left( a+\frac{1}{b} \right)}^{x}}\times {{\left( a-\frac{1}{b} \right)}^{y}}}{{{\left( b+\frac{1}{a} \right)}^{x}}{{\left( b-\frac{1}{a} \right)}^{y}}}.\]
  A)
   \[\frac{a}{b}\]                  done clear
  B)
          \[{{\left( \frac{a}{b} \right)}^{x}}\]          done clear
  C)
          \[{{\left( \frac{a}{b} \right)}^{y}}\]          done clear
  D)
          \[{{\left( \frac{a}{b} \right)}^{x+y}}\] done clear
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• question_answer14)
  By what number should we multiply \[{{(-8)}^{-1}}\]to obtain a product equal to \[{{10}^{-1}}?\]
  A)
   \[\frac{-1}{5}\]                 done clear
  B)
          \[\frac{-4}{5}\] done clear
  C)
   \[\frac{-3}{5}\]                 done clear
  D)
           \[\frac{-2}{5}\] done clear
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• question_answer15)
  Find the value of \[({{2013}^{o}}-{{2012}^{o}})\times (2013+2012).\]
  A)
   4025      done clear
  B)
          1                             done clear
  C)
   0                             done clear
  D)
          -1 done clear
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• question_answer16)
  If \[{{a}^{x}}=b,\,{{b}^{y}}=C,\,{{C}^{z}}=a,\]find the value of \[xyz.\]
  A)
   0                             done clear
  B)
          1             done clear
  C)
   -1                           done clear
  D)
   2 done clear
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• question_answer17)
  What is the value of \[{{20}^{-3}}\times {{25}^{2}}\times {{20}^{3}}\times {{25}^{-4}}?\]
  A)
   \[\frac{1}{625}\]              done clear
  B)
          \[\frac{1}{400}\]              done clear
  C)
          400                        done clear
  D)
          625 done clear
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• question_answer18)
  Find \['x'\]such that \[{{9}^{x+2}}={{3}^{3x-1}}.\]
  A)
   7                             done clear
  B)
          6             done clear
  C)
   5                             done clear
  D)
          4 done clear
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• question_answer19)
  Find the value of \[\frac{{{a}^{m+n}}\times {{a}^{n+l}}\times {{a}^{l+m}}}{{{({{a}^{m}}\times {{a}^{n}}\times {{a}^{l}})}^{2}}}.\]
  A)
   0                             done clear
  B)
          -1                           done clear
  C)
          \[4+m\]               done clear
  D)
          1 done clear
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• question_answer20)
  Which of the following is the exponential form of \[\frac{{{20}^{-2}}\times {{20}^{-2}}\times {{20}^{-2}}}{20}?\]
  A)
  \[{{20}^{-5}}\]                   done clear
  B)
         \[{{20}^{-6}}\]   done clear
  C)
  \[~{{20}^{-7}}~\]              done clear
  D)
         \[~{{20}^{-1}}~\] done clear
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• question_answer21)
  What is the value of \[\frac{1}{1+{{a}^{(n-m)}}}+\frac{1}{1+{{a}^{(m-n)}}}?\]
  A)
   \[{{a}^{m-n}}\]                done clear
  B)
          \[{{a}^{n-m}}\]                done clear
  C)
   \[-1\]                    done clear
  D)
          1 done clear
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• question_answer22)
  Simplify \[({{6}^{1}}-{{8}^{-1}})+{{({{2}^{-1}}-{{3}^{-1}})}^{-1}}.\]
  A)
   40                          done clear
  B)
          30                          done clear
  C)
   20                          done clear
  D)
          50 done clear
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• question_answer23)
  If \[{{x}^{{{m}^{2}}-6}}={{x}^{19}},\]find the value of ?m?.
  A)
   6                             done clear
  B)
          7                             done clear
  C)
                          5                             done clear
  D)
          3 done clear
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• question_answer24)
  If \[{{3}^{x}}=27,\]what is the value of \[{{3}^{x-3}}?\]
  A)
   0                             done clear
  B)
          1                             done clear
  C)
   2                             done clear
  D)
          3 done clear
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• question_answer25)
  Find the value of \[{{(-1)}^{2013}}.\]
  A)
   0                             done clear
  B)
          -1                           done clear
  C)
   1                             done clear
  D)
          2 done clear
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• question_answer26)
  If  \[\sqrt{{{9}^{x}}}=81.\]find the value of \[x.\]
  A)
   2                             done clear
  B)
          4                             done clear
  C)
          3                             done clear
  D)
          9 done clear
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• question_answer27)
  Find the value of \[(0.0001){{(0.0001)}^{\frac{3}{4}}}.\]
  A)
   0.1                         done clear
  B)
          0.01                       done clear
  C)
   0.001    done clear
  D)
          0.0001 done clear
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• question_answer28)
  If \[{{2}^{x-y}}=16\]and \[{{2}^{x+y}}=64,\]find the values of \[x\]and \[y.\]
  A)
   3, 2                        done clear
  B)
          4, 2                        done clear
  C)
   \[5,1\]                  done clear
  D)
         \[6,3\] done clear
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• question_answer29)
  What is the product of \[\left( \frac{{{x}^{a}}}{{{x}^{b}}} \right).\left( \frac{{{x}^{c}}}{{{x}^{a}}} \right).\left( \frac{{{x}^{b}}}{{{x}^{c}}} \right)?\]
  A)
   -1                           done clear
  B)
          1                             done clear
  C)
   0                             done clear
  D)
          \[{{x}^{a+b+c}}\] done clear
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• question_answer30)
  Find the value of \[{{(256)}^{0.16}}\times {{(256)}^{0.09}}.\]
  A)
   4                             done clear
  B)
          16                          done clear
  C)
   64                          done clear
  D)
          256.25                  done clear
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• question_answer31)
  Identify the value of \[1-{{(-0.3)}^{3}}.\]
  A)
   0.73                       done clear
  B)
          0.973    done clear
  C)
          1.027    done clear
  D)
          1.27 done clear
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• question_answer32)
  If \[{{a}^{m+n}}={{a}^{mn}}.\]find the value of \[m(n-2)+n(m-2).\]
  A)
   1                             done clear
  B)
          -1                           done clear
  C)
   0                             done clear
  D)
          ½ done clear
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• question_answer33)
  Find the value of \[{{81}^{\frac{3}{4}}}\times {{64}^{\frac{-2}{3}}}\div {{({{3}^{6}}\times {{2}^{4}})}^{\frac{1}{2}}}.\]
  A)
   \[\frac{1}{8}\]                   done clear
  B)
          \[\frac{1}{16}\]                done clear
  C)
   \[\frac{1}{12}\]                done clear
  D)
          \[\frac{1}{64}\] done clear
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• question_answer34)
  What is the value of \[{{5}^{333}}+{{25}^{222}}-{{125}^{1111}}-{{625}^{111}}?\]
  A)
   1                             done clear
  B)
          25          done clear
  C)
   125                        done clear
  D)
          0 done clear
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• question_answer35)
  If \[{{\left( \frac{1}{5} \right)}^{3\gamma }}=0.008,\]find the value of \[{{(0.25)}^{\gamma }}.\]
  A)
   1.00                       done clear
  B)
          0.25                       done clear
  C)
   0.0625                  done clear
  D)
   0.125 done clear
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• question_answer36)
  If\[x={{a}^{m+n}}{{b}^{l}},y={{a}^{n+l}}{{b}^{m}},z={{a}^{l+m}}{{b}^{n}},\]find \[{{x}^{m-n}}\times {{y}^{n-l}}\times {{z}^{l-m}}.\]
  A)
   0                             done clear
  B)
          -1                           done clear
  C)
   1                             done clear
  D)
          2 done clear
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• question_answer37)
  If \[\frac{{{4}^{5}}+{{4}^{5}}+{{4}^{5}}+{{4}^{5}}}{{{2}^{5}}+{{2}^{5}}}\times \frac{{{6}^{5}}+{{6}^{5}}+{{6}^{5}}+{{6}^{5}}+{{6}^{5}}+{{6}^{5}}}{{{3}^{5}}+{{3}^{5}}+{{3}^{5}}}={{8}^{n}},\]find the value of ?n?.
  A)
   1                             done clear
  B)
          2                             done clear
  C)
   3                             done clear
  D)
          4 done clear
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• question_answer38)
  Find the value of \[\frac{{{(243)}^{0.13}}\times {{(243)}^{0.07}}}{{{(7)}^{0.25}}\times {{(49)}^{0.075}}\times {{(343)}^{0.2}}}.\]
  A)
   \[\frac{3}{7}\]                   done clear
  B)
          \[\frac{7}{3}\]                   done clear
  C)
   \[1\frac{3}{7}\]                done clear
  D)
          \[2\frac{2}{7}\] done clear
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• question_answer39)
  If \[{{4}^{44}}+{{4}^{44}}+{{4}^{44}}+{{4}^{44}}={{4}^{x}},\]what is the value of \['x'\,?\]
  A)
   45                          done clear
  B)
          44          done clear
  C)
   176                        done clear
  D)
          11 done clear
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