How do you simplify #(4p^2)^8 / (4p^2)^6 #? Algebra Exponents and Exponential Functions Exponential Properties Involving Quotients 1 Answer Don't Memorise Mar 24, 2016 #= 16 p^ (4)# Explanation: #((4p^2)^8) / ((4p^2)^6)# By property: #color(blue)((a^m))^n = a ^(mn)# #((4p^2)^8) / ((4p^2)^6)= ((4^8p^(2 * 8 ) )) / ((4^ 6 p^( 2 * 6))# #= ((4^8p^ 16 )) / ((4^ 6 p^12)# #= (4^8 / 4 ^6) * (( p^ 16 )) / ((p^12)# By property: #color(blue)(a^m / a ^n = a ^(m-n)# #= 4^((8 - 6 ) * ( p^ (16 -12 ))# #= 4^(2 ) p^ (4)# #= 16 p^ (4)# 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 1319 views around the world You can reuse this answer Creative Commons License