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Question Number 50011 by ggny last updated on 13/Dec/18

Answered by tanmay.chaudhury50@gmail.com last updated on 13/Dec/18

1)(((13)^4 ×(3×2)^3 ×2^4 ×((1/2))^6 )/(3^3 ×13^3 )) =((13^4 )/(13^3 ))×(3^3 /3^3 )×((2^3 ×2^4 )/2^6 ) =13×2=26

$$\left.\mathrm{1}\right)\frac{\left(\mathrm{13}\right)^{\mathrm{4}} ×\left(\mathrm{3}×\mathrm{2}\right)^{\mathrm{3}} ×\mathrm{2}^{\mathrm{4}} ×\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{6}} }{\mathrm{3}^{\mathrm{3}} ×\mathrm{13}^{\mathrm{3}} } \\ $$$$=\frac{\mathrm{13}^{\mathrm{4}} }{\mathrm{13}^{\mathrm{3}} }×\frac{\mathrm{3}^{\mathrm{3}} }{\mathrm{3}^{\mathrm{3}} }×\frac{\mathrm{2}^{\mathrm{3}} ×\mathrm{2}^{\mathrm{4}} }{\mathrm{2}^{\mathrm{6}} } \\ $$$$=\mathrm{13}×\mathrm{2}=\mathrm{26} \\ $$

Answered by tanmay.chaudhury50@gmail.com last updated on 13/Dec/18

2)((11^6 )/(11^6 ))×(((2^2 ×3)^2 ×3^3 )/((3×2)^2 ×(3^2 )×((1/2))^2 )) =(2^4 /2^2 )×2^2 ×(3^(2+3) /3^(2+2) ) =16×3=48

$$\left.\mathrm{2}\right)\frac{\mathrm{11}^{\mathrm{6}} }{\mathrm{11}^{\mathrm{6}} }×\frac{\left(\mathrm{2}^{\mathrm{2}} ×\mathrm{3}\right)^{\mathrm{2}} ×\mathrm{3}^{\mathrm{3}} }{\left(\mathrm{3}×\mathrm{2}\right)^{\mathrm{2}} ×\left(\mathrm{3}^{\mathrm{2}} \right)×\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} } \\ $$$$=\frac{\mathrm{2}^{\mathrm{4}} }{\mathrm{2}^{\mathrm{2}} }×\mathrm{2}^{\mathrm{2}} ×\frac{\mathrm{3}^{\mathrm{2}+\mathrm{3}} }{\mathrm{3}^{\mathrm{2}+\mathrm{2}} } \\ $$$$=\mathrm{16}×\mathrm{3}=\mathrm{48} \\ $$

Answered by tanmay.chaudhury50@gmail.com last updated on 13/Dec/18

3)((17^4 )/(17^4 ))×(3^6 /3^4 )×(1/(((1/2))^5 ))×(1/2^3 ) =3^2 ×(2^5 /2^3 ) =3^2 ×2^(5−3) =3^2 ×2^2 =9×4=36

$$\left.\mathrm{3}\right)\frac{\mathrm{17}^{\mathrm{4}} }{\mathrm{17}^{\mathrm{4}} }×\frac{\mathrm{3}^{\mathrm{6}} }{\mathrm{3}^{\mathrm{4}} }×\frac{\mathrm{1}}{\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{5}} }×\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{3}} } \\ $$$$=\mathrm{3}^{\mathrm{2}} ×\frac{\mathrm{2}^{\mathrm{5}} }{\mathrm{2}^{\mathrm{3}} } \\ $$$$=\mathrm{3}^{\mathrm{2}} ×\mathrm{2}^{\mathrm{5}−\mathrm{3}} \\ $$$$=\mathrm{3}^{\mathrm{2}} ×\mathrm{2}^{\mathrm{2}} \\ $$$$=\mathrm{9}×\mathrm{4}=\mathrm{36} \\ $$

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