The question actually being asked is what is the coefficient of [tex]x^6[/tex] in
[tex] (x^2 - \frac 2 7)^7 [/tex]
Since
[tex](x^2)^3=x^6[/tex]
we're interested in the [tex]{7 \choose 3}a^3 b^4[/tex] term of the expansion of [tex](a+b)^7[/tex]
So our term of interest is
[tex]{7 \choose 3} (x^2)^3 (-\frac 2 7)^4 = \dfrac{7(6)(5)}{3(2)(1)} \dfrac{2^4}{7^4} x^6 = \dfrac{2^4(5)}{7^3} x^6 = \dfrac{80}{343} x^6[/tex]
Answer:
[tex]\quad \dfrac{80}{343}[/tex]
