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Question Number 10627 by pan123 last updated on 20/Feb/17

60^(15) ×30^8 ×35^6 ×60^(15) =?

$$\mathrm{60}^{\mathrm{15}} ×\mathrm{30}^{\mathrm{8}} ×\mathrm{35}^{\mathrm{6}} ×\mathrm{60}^{\mathrm{15}} =? \\ $$

Answered by mrW1 last updated on 20/Feb/17

60=2^2 ×3×5 30=2×3×5 35=5×7 60^(15) ×30^8 ×35^6 ×60^(15) =60^(30) ×30^8 ×35^6 =(2^2 ×3×5)^(30) ×(2×3×5)^8 ×(5×7)^6 =2^(2×30+8) ×3^(30+8) ×5^(30+8+6) ×7^6 =2^(68) ×3^(38) ×5^(44) ×7^6

$$\mathrm{60}=\mathrm{2}^{\mathrm{2}} ×\mathrm{3}×\mathrm{5} \\ $$$$\mathrm{30}=\mathrm{2}×\mathrm{3}×\mathrm{5} \\ $$$$\mathrm{35}=\mathrm{5}×\mathrm{7} \\ $$$$ \\ $$$$\mathrm{60}^{\mathrm{15}} ×\mathrm{30}^{\mathrm{8}} ×\mathrm{35}^{\mathrm{6}} ×\mathrm{60}^{\mathrm{15}} \\ $$$$=\mathrm{60}^{\mathrm{30}} ×\mathrm{30}^{\mathrm{8}} ×\mathrm{35}^{\mathrm{6}} \\ $$$$=\left(\mathrm{2}^{\mathrm{2}} ×\mathrm{3}×\mathrm{5}\right)^{\mathrm{30}} ×\left(\mathrm{2}×\mathrm{3}×\mathrm{5}\right)^{\mathrm{8}} ×\left(\mathrm{5}×\mathrm{7}\right)^{\mathrm{6}} \\ $$$$=\mathrm{2}^{\mathrm{2}×\mathrm{30}+\mathrm{8}} ×\mathrm{3}^{\mathrm{30}+\mathrm{8}} ×\mathrm{5}^{\mathrm{30}+\mathrm{8}+\mathrm{6}} ×\mathrm{7}^{\mathrm{6}} \\ $$$$=\mathrm{2}^{\mathrm{68}} ×\mathrm{3}^{\mathrm{38}} ×\mathrm{5}^{\mathrm{44}} ×\mathrm{7}^{\mathrm{6}} \\ $$$$ \\ $$

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