12 x^{5} y^{7} and 7 x^{2} y^{9}

19x^7y^16

Step-by-step explanation:

And usually means to add, so combine your like terms:

12x^5y^7 + 7x^2y^9

12 + 7 = 19

x^5 + x^2 = x^7

y^7 + y^9 = y^16

Step-by-step explanation:

(12x⁵ y⁷) * (7x²y⁹) = (12*7) * (x⁽⁵⁺²⁾ ) (y⁽⁷⁺⁹⁾)

                            = 84x⁷y¹⁶

In exponents multiplication, if base are same, then add the powers.

xᵃ * xᵇ = x⁽ᵃ⁺ᵇ⁾

1) Given
2) Adding segments AB and BC together gives AC (Addition postulate, not too sure about the terminology) 
3) Segment Addition postulate 
4) Segment Addition postulate(Knowing that AC=BD, the distance between BC and CD add up to BD, shown in #3. AB and BC add together to give AC) 
5) Subtraction property of Equality 

Hope I helped :)