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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)

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

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

$(2\times5)^{5}=10^5$

$(vii)\:a^{4}\times b^{4}$

can be simplified as $(ab)^4$

$(viii)\:(3^{4})^{3}$

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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