7th Class Mathematics Exponents and Power Question Bank

done Exponents and Powers Total Questions - 25

• question_answer1)
  \[{{2}^{3}}+{{2}^{3}}+{{2}^{3}}+{{2}^{3}}\]is equal to ____.     
  A)
   \[{{2}^{5}}\]                                   done clear
  B)
   \[{{2}^{12}}\]                     done clear
  C)
                      281                 done clear
  D)
          216                             done clear
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• question_answer2)
   The value of \[\frac{{{\left( -\frac{1}{2} \right)}^{5}}}{{{\left( -\frac{1}{2} \right)}^{4}}}+\frac{\left( -\frac{1}{8} \right)}{\left( -\frac{1}{4} \right)}\] is ____.
  A)
   2                                 done clear
  B)
   0                     done clear
  C)
          1                     done clear
  D)
         \[-1\]                            done clear
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• question_answer3)
  \[\left\{ {{\left( \frac{1}{3} \right)}^{-3}}-{{\left( \frac{1}{2} \right)}^{-3}} \right\}\div {{\left( \frac{1}{4} \right)}^{-3}}=?\]
  A)
   \[\frac{19}{64}\]                                done clear
  B)
   \[\frac{64}{19}\]                    done clear
  C)
          \[\frac{27}{16}\]                    done clear
  D)
          \[\frac{16}{27}\]                    done clear
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• question_answer4)
  The value of \[(-8)\times (-8)\times (-8)\times (-8)+(-8)\]\[\times (-8)\times (-8)\times (-8)\] is ____.                         
  A)
   \[-2{{(8)}^{5}}\]                 done clear
  B)
   \[-{{(2)}^{16}}\]     done clear
  C)
          \[-{{(4)}^{8}}\]            done clear
  D)
          All of these                  done clear
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• question_answer5)
  If \[{{\left( \frac{5}{3} \right)}^{-5}}\times {{\left( \frac{5}{3} \right)}^{11}}={{\left( \frac{5}{3} \right)}^{8+x}},\]  then x=?    
  A)
   \[\frac{-1}{2}\]                                  done clear
  B)
   \[-2\]               done clear
  C)
   \[2\]                 done clear
  D)
   \[\frac{1}{2}\]                        done clear
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• question_answer6)
  The value of \[\left( \frac{{{a}^{-2}}\times {{b}^{-3}}}{{{a}^{-3}}\times {{b}^{-4}}} \right)\] is ________.
  A)
   \[{{a}^{-1}}\times b\]                     done clear
  B)
   \[a\times {{b}^{-1}}\]         done clear
  C)
          \[{{(ab)}^{-1}}\]            done clear
  D)
          \[ab\]               done clear
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• question_answer7)
  \[{{\left\{ {{\left( \frac{3}{4} \right)}^{-1}}-{{\left( \frac{1}{4} \right)}^{-1}} \right\}}^{-1}}=?\]
  A)
   \[\frac{3}{8}\]                                    done clear
  B)
   \[\frac{-3}{8}\]                      done clear
  C)
   \[\frac{8}{3}\]                        done clear
  D)
   \[\frac{-8}{3}\]                                  done clear
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• question_answer8)
  Select the CORRECT match.
  A)

  Exponent	Base	Value
  34	3	87

                  done clear
  B)

  Exponent	Base	Value
  25	5	32

                  done clear
  C)

  Exponent	Base	Value
  43	4	64

                  done clear
  D)

  Exponent	Base	Value
  52	5	125

  done clear
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• question_answer9)
  If \[{{\left( \frac{5}{9} \right)}^{4}}\times {{\left( \frac{5}{9} \right)}^{-10}}={{\left( \frac{5}{9} \right)}^{-4}}{{\left( \frac{5}{9} \right)}^{2a-1}},\]then the value of a is _____.
  A)
   1                                 done clear
  B)
   \[\frac{-5}{2}\]                      done clear
  C)
   \[\frac{-5}{4}\]                      done clear
  D)
          \[\frac{-1}{2}\]                      done clear
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• question_answer10)
  Which of the following is equivalent to \[7.7\times {{10}^{-6}}\]?
  A)
   \[0.00000077\]            done clear
  B)
   \[0.0000077\]              done clear
  C)
   \[0.000077\]                done clear
  D)
   \[0.00077\]                  done clear
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• question_answer11)
  If \[{{\left( \frac{3}{2} \right)}^{2}}\times {{\left( \frac{3}{2} \right)}^{a+5}}={{\left( \frac{3}{2} \right)}^{8}},\]then a=____.
  A)
   \[-1\]                           done clear
  B)
   0                     done clear
  C)
          1                     done clear
  D)
          2                     done clear
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• question_answer12)
  The number which is multiplied by \[{{(-8)}^{-1}}\]to obtain a product equal to \[{{10}^{-1}}\] is ____.
  A)
   \[-\frac{4}{5}\]                                  done clear
  B)
   \[-\frac{3}{5}\]                      done clear
  C)
   \[-\frac{1}{5}\]          done clear
  D)
          \[-\frac{5}{4}\]          done clear
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• question_answer13)
  The value of \[\frac{{{6}^{12}}\times {{(35)}^{28}}\times {{(15)}^{16}}}{{{(14)}^{12}}\times {{(21)}^{11}}\times {{5}^{28}}}\] is??.
  A)
   \[{{2}^{6}}\times {{3}^{16}}\times {{5}^{12}}\]       done clear
  B)
   \[{{3}^{17}}\times {{5}^{16}}\times {{7}^{5}}\]                   done clear
  C)
  \[{{2}^{6}}\times {{5}^{16}}\times {{7}^{12}}\]    done clear
  D)
          \[{{2}^{7}}\times {{3}^{17}}\times {{7}^{5}}\]         done clear
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• question_answer14)
  The value of \[{{a}^{b}}-{{b}^{a}},\]if \[a=3,\text{ }b=7\]is
  A)
   1825                           done clear
  B)
   1840   done clear
  C)
          1844               done clear
  D)
          1850   done clear
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• question_answer15)
  The value of \[{{\left( \frac{23}{25} \right)}^{0}}\times {{\left( \frac{-1}{2} \right)}^{5}}\times {{2}^{3}}\times {{\left( \frac{3}{4} \right)}^{2}}\]is
  A)
   \[-\frac{9}{64}\]           done clear
  B)
   \[\frac{9}{64}\]                      done clear
  C)
   \[\frac{64}{9}\]                      done clear
  D)
          \[-\frac{64}{9}\]        done clear
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• question_answer16)
  A rectangular piece of land is to be sold off in smaller pieces. The total area of the land is 217 sq. miles. The pieces to the cut out are 162 sq. miles in size. How many smaller pieces of the land can be sold at the given size?              
  A)
   215                 done clear
  B)
   164                 done clear
  C)
          29                   done clear
  D)
          None of these              done clear
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• question_answer17)
  Pooja spends about Rs.40000 each month on utensils hold. If she has about \[1\times {{10}^{8}}\] utensils, what is the total amount of money (in Rs.) spent on the households in one month?
  A)
   \[40\times {{10}^{8}}\]                   done clear
  B)
   40000 done clear
  C)
          \[4.0\times {{10}^{14}}\]       done clear
  D)
         \[4.0\times {{10}^{12}}\]     done clear
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• question_answer18)
  All the planets revolve around the Sun in elliptical orbits. Uranus's farthest distance from the Sun is approximately \[3.004\times {{10}^{9}}\text{ }km\]and its closest distance is approximately \[2.7499\times {{10}^{9}}km\]km. What is the average distance of Uranus from the Sun?       
  A)
   \[(2.476\times {{10}^{9}})\,km\]                  done clear
  B)
   \[(2.8765\times {{10}^{9}})\,km\]                 done clear
  C)
   \[(2.876\times {{10}^{8}})\,km\]                done clear
  D)
   None of these   done clear
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• question_answer19)
                  There are three places A, B, C in a straight line as shown below. If distance between place A and B is \[(2.4\times {{10}^{6}})m\] and distance between 8 and C is \[(5.2\times {{10}^{5}})m,\] then find the distance between place A and C in standard form.
  A)
               \[(292\times {{10}^{6}})km\]             done clear
  B)
               \[(2.92\times {{10}^{6}})km\] done clear
  C)
               \[(292\times {{10}^{5}})km\] done clear
  D)
               \[(2.92\times {{10}^{4}})\,m\] done clear
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• question_answer20)
  Mr Gupta asked two of his students to solve the expression \[{{\left( \frac{9{{a}^{3}}{{b}^{-8}}}{81{{a}^{-5}}{{b}^{2}}} \right)}^{-\frac{1}{2}}}\]and write the answer on blackboard. Aryan wrote the answer as \[3{{a}^{-4}}{{b}^{5}}\] whereas Ayan wrote the answer as \[\frac{3{{b}^{5}}}{{{a}^{4}}}\].  Who wrote the correct answer?
  A)
   Aryan done clear
  B)
   Ayan done clear
  C)
   Both of them done clear
  D)
   None of these done clear
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• question_answer21)
  Match the following.  

  Column-l	Column-II
  (P) \[\left[ {{({{5}^{3}})}^{2}}\times {{5}^{5}} \right]\div {{5}^{9}}\]	(i) \[{{(-6)}^{3}}\]
  (Q) \[{{(-6)}^{5}}\div {{(6)}^{2}}\]	(ii) 2
  (R) \[({{5}^{0}}+{{3}^{0}})\div ({{8}^{0}})\]	(iii) 1
  (S) \[{{(7/19)}^{0}}\]	(iv) 25

  A)
   (P)\[\to \](i), (Q)\[\to \](ii), (R)\[\to \](iii), (S)\[\to \](iv) done clear
  B)
   (P)\[\to \](ii), (Q)\[\to \](iii), (r)\[\to \](iv), (S)\[\to \](i) done clear
  C)
   (P)\[\to \](iv), (Q)\[\to \](i). (R)\[\to \](ii), (S)\[\to \](iii) done clear
  D)
   (P)\[\to \](iv), (Q)\[\to \](ii), (R)\[\to \](i), (S)\[\to \](iii) done clear
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• question_answer22)
  Compare the following and put the correct sign.                                      

  I. \[{{({{3}^{2}})}^{3}}\]

  II. \[{{({{8}^{4}})}^{\frac{1}{2}}}\]

  III. \[{{({{3}^{1/3}})}^{9}}\]

  A)

  I	II	III
  >	<	=

                  done clear
  B)

  I	II	III
  <	=	>

                  done clear
  C)

  I	II	III
  <	>	>

                  done clear
  D)

  I	II	III
  <	>	>

  done clear
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• question_answer23)
  Which of the following statements is true?

  Statement 1: \[x={{\left[ \frac{2}{3} \right]}^{4}}\div {{\left[ \frac{2}{3} \right]}^{2}},\] then value of \[{{x}^{2}}+2x+3\]is 0.

  Statement 2: If \[{{\left[ -\frac{1}{2} \right]}^{4}}\times {{(-2)}^{8}}={{(-2)}^{4x}}\] then\[x=1\].

  A)
   Only Statement-1                  done clear
  B)
   Only Statement-2 done clear
  C)
   Both Statement-1 and Statement-2 done clear
  D)
   Neither Statement-1 nor Statement-2 done clear
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• question_answer24)
  State T for true and T' for false.

  (P) If x and y are non-zero rational numbers and m is a positive integer, then \[{{x}^{m}}\times {{y}^{m}}={{(xy)}^{2m}}\] and \[{{x}^{m}}\div {{y}^{m}}={{\left( \frac{x}{y} \right)}^{1}}.\]

  (Q) Standard form of 38000000 is\[3.8\times {{10}^{7}}\].

  (R) The base and power in \[{{(-16\times 2)}^{4}}\]is \[-32\] and 4 respectively.

  (S) \[{{6}^{2}}\] is greater than \[{{2}^{6}}\].

  A)

  (P)	(Q)	(R)	(S)
  T	F	F	T

  done clear
  B)

  (P)	(Q)	(R)	(S)
  F	T	T	F

  done clear
  C)

  (P)	(Q)	(R)	(S)
  F	T	F	T

  done clear
  D)

  (P)	(Q)	(R)	(S)
  T	F	T	F

  done clear
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• question_answer25)
  Fill in the blanks.

  (i) A number is said to be in the ___ form. if it is expressed as the product of a number between 1 and 10 and the integral power of 10.

  (ii)  \[{{2}^{0}}\times {{3}^{0}}+{{1}^{0}}\times 3=\_\_\_\]

  (iii) \[\left( {{\left( {{2}^{2}} \right)}^{2}}\times {{7}^{2}} \right)\div \left( {{8}^{3}}\times 7 \right)=\_\_\_\_\_\_\_\_\_.\]

  A)

  (i)	(ii)	(iii)
  Standard	4	\[7\times {{2}^{-5}}\]

                  done clear
  B)

  (i)	(ii)	(iii)
  Exponential	4	\[7\times {{2}^{-4}}\]

                  done clear
  C)

  (i)	(ii)	(iii)
  Exponential	2	\[7\times {{2}^{5}}\]

                  done clear
  D)

  (i)	(ii)	(iii)
  Standard	2	\[7\times {{2}^{4}}\]

  done clear
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