Find the value - older math olympiad question Help :)

[Guest]

Find the value [tex]a^3b^7c^{14}=[/tex]
[tex]a^3b^2c=108[/tex],
[tex]a^2b^3c^5=240[/tex]

[Guest]

I received an answer 128 000 .

[kasia]

Can you show some work? Thanks

[Guest]

We notice that :

[tex]\frac{(a^{2}b^{3}c^{5})^{3}}{a^{3}b^{2}c}[/tex]=[tex]\frac{a^{6}b^{9}c^{15}}{a^{3}b^{2}c}[/tex]

We received [tex]\frac{(a^{2}b^{3}c^{5})^{3}}{a^{3}b^{2}c}[/tex]=[tex]a^{3}[/tex][tex]b^{7}[/tex][tex]c^{14}[/tex]

[tex]\frac{240^{3}}{108}[/tex]=[tex]a^{3}[/tex][tex]b^{7}[/tex][tex]c^{14}[/tex]

[tex]a^{3}[/tex][tex]b^{7}[/tex][tex]c^{14}[/tex]=[tex]\frac{13 824 000}{108}[/tex]=128 000

[kasia]

thank you!