Which values of a and b make the following equation true? (5x7y2)(-4x4y5)=-20xayb

Answer:The values of a and b are a = 11 , b = 7Step-by-step explanation:* Lets explain how to solve the problem* In the exponential functions we have some rules1-  In multiplication if they have same base we add  the power# Ex: b^m  ×  b^n  =  b^(m + n) ⇒ b is the base , m and n are the powers2- In division if they have same base we subtract  the power# Ex: b^m  ÷  b^n =  b^(m – n) ⇒ b is the base , m and n are the powers3- If we have power over power we multiply them# Ex: (b^m)^n = b^(mn) ⇒ b is the base , m and n are the powers* Lets solve the problem∵ The equation is [tex](5x^{7}y^{2})(-4x^{4}y^{5})=-20x^{a}y^{2}[/tex] ⇒ (1)- At first multiply the coefficients∵ -4 × 5 = -20- Multiply the base x∵ [tex](x^{7})(x^{4})=x^{7+4}=x^{11}[/tex]- Multiply the base y∵ [tex](y^{2})(y^{5})=y^{2+5}=y^{7}[/tex]∴ [tex](5x^{7}y^{2})(-4x^{4}y^{5})=-20x^{11}y^{7}[/tex] ⇒ (2)- By comparing (1) and (2)∴ a = 11 and b = 7* The values of a and b are a = 11 , b = 7