Simplify the following index question, expressing your answer with positive exponents?

Question

#(x^3yz^-2times2(x^3y^-2z)^2)/(xyz^-1)#

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Answer 1 · 2017-10-10T14:28:58

#(2 x^(8)z)/ y^(4)#

#(x^3yz^-2times2(x^3y^-2z)^2)/(xyz^-1)#

Using rule : #(a^m)n = a^(mn)#

#=>x^3yz^-2times2(x^(3\times2)y^(-2times2)z^2)/(xyz^-1)#

#=>(2 x^3yz^-2times(x^6y^-4z^2))/(xyz^-1)#

#=>(2 x^3yz^-2timesx^6y^-4z^2)/(xyz^-1)#

Using rule: #a^m \times a^n = a^(m+n)#

#=>(2 x^(3+6)y^(1-4)z^(-2+2))/(xyz^-1)#

#=>(2 x^(9)y^(-3)z^(0))/(xyz^-1)#

Using rule : # a^m/a^n = a^(m-n)#

#=>(2 x^(9-1)y^(-3-1)z^(0+1))#

#=>(2 x^(8)y^(-4)z^(1))#

Using rule: #a^-m =1/a^m #

#=>(2 x^(8)z^(1))/ y^(4)#