• # question_answer9) Using laws of exponents, simplify and write the answer in exponential form: (i) ${{3}^{2}}\times {{3}^{4}}\times {{3}^{8}}$                   (ii) ${{6}^{15}}\div {{6}^{10}}$                  (iii) ${{a}^{3}}\times {{a}^{2}}$                        (iv) ${{7}^{x}}\times {{7}^{2}}$ (v) ${{({{5}^{2}})}^{3}}\div {{5}^{3}}$                    (vi) ${{2}^{5}}\times {{5}^{5}}$                                (vii) ${{a}^{4}}\times {{b}^{4}}$                       (viii) ${{({{3}^{4}})}^{3}}$ (ix) $({{2}^{20}}\div {{2}^{15}})\times {{2}^{3}}$

(i) ${{\mathbf{3}}^{\mathbf{2}}}\mathbf{\times }{{\mathbf{3}}^{\mathbf{4}}}\mathbf{\times }{{\mathbf{3}}^{\mathbf{8}}}$                 ${{3}^{2}}\times {{3}^{4}}\times {{3}^{8}}={{3}^{2+4}}\times {{3}^{8}}$               $\left| {{a}^{m}}\times {{a}^{n}} \right.={{a}^{m+n}}$                 $={{3}^{6}}\times {{3}^{8}}={{3}^{6+8}}={{3}^{14}}$      $\left| {{a}^{m}}\times {{a}^{n}} \right.={{a}^{m+n}}$                 (ii) ${{\mathbf{6}}^{\mathbf{15}}}\mathbf{\div }{{\mathbf{6}}^{\mathbf{10}}}$                            ${{6}^{15}}\div {{6}^{10}}={{6}^{15-10}}$ $={{6}^{5}}$                                     $\left| {{a}^{m}}\div {{a}^{n}} \right.={{a}^{m-n}}$                 (iii) ${{\mathbf{a}}^{\mathbf{3}}}\mathbf{\times }{{\mathbf{a}}^{\mathbf{2}}}$                 ${{a}^{3}}\times {{a}^{2}}={{a}^{3+2}}$                               $\left| {{a}^{m}}\times {{a}^{n}} \right.={{a}^{m+n}}$                 $={{a}^{5}}$                 (iv) ${{\mathbf{7}}^{\mathbf{x}}}\mathbf{\times }{{\mathbf{7}}^{\mathbf{2}}}$                 ${{7}^{x}}\times {{7}^{2}}={{7}^{x+2}}$                               $\left| {{a}^{m}}\times {{a}^{n}} \right.={{a}^{m+n}}$                 (v) ${{\mathbf{(}{{\mathbf{5}}^{\mathbf{2}}}\mathbf{)}}^{\mathbf{3}}}\mathbf{\div }{{\mathbf{5}}^{\mathbf{3}}}$                 ${{({{5}^{2}})}^{3}}\div {{5}^{3}}={{5}^{2\times 3}},{{5}^{3}}$   ${{\left| ({{a}^{m}}) \right.}^{n}}={{a}^{mn}}$                 $={{5}^{6}},{{5}^{3}}={{5}^{6-3}}$                          $\left| {{a}^{m}}\div {{a}^{n}}={{a}^{m-n}} \right.$                 $={{5}^{3}}$                 (vi) ${{\mathbf{2}}^{\mathbf{5}}}\mathbf{\times }{{\mathbf{5}}^{\mathbf{5}}}$                 ${{2}^{5}}\times {{5}^{5}}={{(2\times 5)}^{5}}$                $\left| {{a}^{m}}\times {{b}^{m}}={{(ab)}^{m}} \right.$ $={{10}^{5}}$                 (vii) ${{\mathbf{a}}^{\mathbf{4}}}\mathbf{\times }{{\mathbf{b}}^{\mathbf{4}}}$                 ${{a}^{4}}\times {{b}^{4}}={{(ab)}^{4}}$                             $\left| {{a}^{m}}\times {{b}^{m}}={{(ab)}^{m}} \right.$                 (viii) ${{\mathbf{(}{{\mathbf{3}}^{\mathbf{4}}}\mathbf{)}}^{\mathbf{3}}}$                 ${{({{3}^{4}})}^{3}}={{3}^{4}}^{\times 3}$                          $\left| {{({{a}^{m}})}^{n}} \right.={{a}^{mn}}$                 $={{3}^{12}}$ (ix) $\mathbf{(}{{\mathbf{2}}^{\mathbf{20}}}\mathbf{\div }{{\mathbf{2}}^{\mathbf{15}}}\mathbf{)\times }{{\mathbf{2}}^{\mathbf{3}}}$                 $({{2}^{20}}\div {{2}^{15}})\times {{2}^{3}}={{2}^{20-15}}\times {{2}^{3}}$  $\left| {{a}^{m}}\div {{a}^{n}}={{a}^{m-n}} \right.$                 $={{2}^{5}}\times {{2}^{3}}$                     $={{2}^{5+3}}$                                                $\left| {{a}^{m}}\div {{a}^{n}}={{a}^{m+n}} \right.$                 $={{2}^{8}}$                 (x)  ${{\mathbf{8}}^{\mathbf{t}}}\mathbf{\div }{{\mathbf{8}}^{\mathbf{2}}}$                 ${{8}^{t}}\div {{8}^{2}}={{8}^{t-2}}$                      $\left| {{a}^{m}}\div {{a}^{n}}={{a}^{m-n}} \right.$