How do you simplify #(3y^4)^5/y^-6#?

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Answer 1 · 2018-06-04T16:39:03

#243y^26#

We get
#(3y^4)^5=3^5y^20#
so
#(3^5y^20)/y^(-6)=243*y^26#

Answer 2 · 2018-06-04T16:43:31

#=243y^(26)#

First rule of exponents we use is:

#(a^n)^m = a^(n*m)#

#=(3y^4)^5/y^-6#

#=(3^(1*5)y^(4*5))/y^-6#

#=(3^(5)y^20)/y^-6#

#=(243y^20)/y^-6#

New we use the rule for quotients of exponents:

#a^n/a^m = a^(n-m)#

#=(243y^20)/y^-6#

#=243y^(20-(-6))#

#=243y^(26)#