question_answer 10)

Say true or false and justify your answer: (i) \[10\times {{10}^{11}}={{100}^{11}}\]               (ii) \[{{2}^{3}}>{{5}^{2}}\]             (iii) \[{{2}^{3}}\times {{3}^{2}}={{6}^{5}}\]                       (iv) \[{{3}^{0}}={{(1000)}^{0}}\].

Answer:

                (i) \[10\times {{10}^{11}}={{10}^{1}}\times {{10}^{11}}={{10}^{1+11}}\] \[={{10}^{12}}\]                 \[{{100}^{11}}={{(10\times 10)}^{11}}={{({{10}^{2}})}^{11}}\]                 \[={{10}^{22}}\]                 So, \[10\times {{10}^{11}}\ne {{100}^{11}}\] \[\therefore \]  \[10\times {{10}^{11}}={{100}^{11}}\]is false.                 (ii) \[{{2}^{3}}=2\times 2\times 2=98\]                 \[{{5}^{2}}=5\times 5=25\] \[\because \]     \[8>/25\] \[\therefore \]  \[{{2}^{3}}>{{5}^{2}}\]is false. (iii) \[{{6}^{5}}={{(2\times 3)}^{5}}={{2}^{5}}\times {{3}^{5}}\] \[\therefore \]  \[{{2}^{3}}\times {{3}^{2}}={{6}^{5}}\]is false.                 (iv) \[{{3}^{0}}=1,{{1000}^{0}}=1\]. \[\therefore \]  \[{{3}^{0}}={{1000}^{0}}\]is true.