How do you simplify (12a^-9b^-4)/( 9a^2b^6)? Algebra Exponents and Exponential Functions Exponential Properties Involving Quotients 1 Answer Don't Memorise Mar 16, 2016 =(4 a^-11 b^-10)/3 Explanation: (12a^-9b^-4)/(9a^2b^6) =(12/9) * ((a^-9b^-4)/(a^2b^6)) =(cancel12/cancel9) * ((a^-9b^-4)/(a^2b^6)) =(4/3) * (a^-9 / a^2 ) * ((b^-4)/(b^6)) as per property: color(blue)(a^m/a^n = a ^(m-n) =(4/3) * (a^(-9 -2) ) * (b^(-4 -6)) =(4/3) * ( a^-11) * (b^-10) =4/3 a^-11 b^-10 =(4 a^-11 b^-10)/3 Answer link Related questions What is the quotient of powers property? How do you simplify expressions using the quotient rule? What is the power of a quotient property? How do you evaluate the expression (2^2/3^3)^3? How do you simplify the expression \frac{a^5b^4}{a^3b^2}? How do you simplify ((a^3b^4)/(a^2b))^3 using the exponential properties? How do you simplify \frac{(3ab)^2(4a^3b^4)^3}{(6a^2b)^4}? Which exponential property do you use first to simplify \frac{(2a^2bc^2)(6abc^3)}{4ab^2c}? How do you simplify (x^5y^8)/(x^4y^2)? How do you simplify [(2^3 *-3^2) / (2^4 * 3^-2)]^2? See all questions in Exponential Properties Involving Quotients Impact of this question 1609 views around the world You can reuse this answer Creative Commons License