Find the Degree 5a^6bc^2+8d^5+7e^6f^2-10g^4h^7

$5 a^{6} b c^{2} + 8 d^{5} + 7 e^{6} f^{2} - 10 g^{4} h^{7}$

Identify the exponents on the variables in each term, and add them together to find the degree of each term.

$5 a^{6} b c^{2} \to 9$

$8 d^{5} \to 5$

$7 e^{6} f^{2} \to 2$

$- 10 g^{4} h^{7} \to 11$

The largest exponent is the degree of the polynomial.

$11$