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14-15-6-45-28-6-

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Question Number 201144 by sts313 last updated on 30/Nov/23
(((14)/(15)))^6 ×(((45)/(28)))^6 =
$$\left(\frac{\mathrm{14}}{\mathrm{15}}\right)^{\mathrm{6}} ×\left(\frac{\mathrm{45}}{\mathrm{28}}\right)^{\mathrm{6}} = \\ $$
Answered by mathlove last updated on 01/Dec/23
(((14)/(15)))^6 ×(((3×15)/(2×14)))^6 =((14^6 )/(15^6 ))×((3^6 ×15^6 )/(2^6 ×14^6 )) =((3/2))^6
$$\left(\frac{\mathrm{14}}{\mathrm{15}}\right)^{\mathrm{6}} ×\left(\frac{\mathrm{3}×\mathrm{15}}{\mathrm{2}×\mathrm{14}}\right)^{\mathrm{6}} =\frac{\cancel{\mathrm{14}^{\mathrm{6}} }}{\cancel{\mathrm{15}^{\mathrm{6}} }}×\frac{\mathrm{3}^{\mathrm{6}} ×\cancel{\mathrm{15}^{\mathrm{6}} }}{\mathrm{2}^{\mathrm{6}} ×\cancel{\mathrm{14}^{\mathrm{6}} }} \\ $$$$=\left(\frac{\mathrm{3}}{\mathrm{2}}\right)^{\mathrm{6}} \\ $$
Answered by Rasheed.Sindhi last updated on 01/Dec/23
Another way (((14)/(15)))^6 ×(((45)/(28)))^6 =(((14^(1) )/(15_(1) ))×((45^(3) )/(28_(2) )))^6 =(3^6 /2^6 )=((729)/(64))
$$\mathrm{Another}\:\mathrm{way} \\ $$$$\left(\frac{\mathrm{14}}{\mathrm{15}}\right)^{\mathrm{6}} ×\left(\frac{\mathrm{45}}{\mathrm{28}}\right)^{\mathrm{6}} =\left(\frac{\cancel{\overset{\mathrm{1}} {\mathrm{14}}}}{\cancel{\underset{\mathrm{1}} {\mathrm{15}}}}×\frac{\cancel{\overset{\mathrm{3}} {\mathrm{45}}}}{\cancel{\underset{\mathrm{2}} {\mathrm{28}}}}\right)^{\mathrm{6}} =\frac{\mathrm{3}^{\mathrm{6}} }{\mathrm{2}^{\mathrm{6}} }=\frac{\mathrm{729}}{\mathrm{64}} \\ $$

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