Sum of the exponents of the variables

By binomial theorem we have $\displaystyle \left(x^7-y^7\right)^{20} = \sum_{k=0}^{20} (-1)^k \binom {20}k \left(x^7 \right)^k \left(y^7 \right)^{20-k}$ . The sum of exponents of $k$ th term is given by $7k + 7(20-k) = 140$ . Since there are 21 terms in the expansion, the sum of exponents for the whole expansion is $140 \times 21 = \boxed{2940}$ .