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1.  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}        (x)\:8^{t}\div 8^{2}

Answers (1)


  (i)\: 3^{2}\times 3^{4}\times 3^{8}      

can be simplified as 3^{(2+4+8)}=3^{14}

  (ii)\: 6^{15}\div 6^{10}       

can be simplified as 6^{(15-10)}=6^{5}

(iii)\: a^{3}\times a^{2}

can be simplified as      a^{(3+2)}=a^{5}  

(iv)\: 7^{x}\times 7^{2}

can be simplified as 7^{(x+2)}=7^{(x+2)}

 (v)\:(5^{2})^{3}\div 5^{3}

can be simplified as  5^{(2\times 3)}\div 5^{(3)}=5^6\div 5^3=5^{6-3}=5^3                

(vi)\:2^{5}\times 5^{5}         

can be simplified as  


(vii)\:a^{4}\times b^{4}       

can be simplified as  (ab)^4


can be simplified as 3^{4\times 3}=3^{12}

 (ix)\:(2^{20}\div 2^{15})\times 2^{3}

can be simplified as     2^{(20-15)}\times 2^3=2^5\times 2^3=2^{(5+3)}=2^8    

(x)\:8^{t}\div 8^{2}

can be simplified as 8^{(t-2)}

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