How do you simplify #((2m)/ n^2)^4#?

2 Answers
Jul 13, 2015

#((2m)/n^2)^4 = (16m^4)/n^8#

You must apply the outside exponent to everything inside the parentheses.

#((2m)/n^2)^4 = (2^4m^4)/(n^2)^4#

We have to repeat the procedure with the denominator.

#(2^4m^4)/(n^2)^4 = (2^4m^4)/n^8#

So

#((2m)/n^2)^4 = (2^4m^4)/n^8=(16m^4)/n^8#

Jul 13, 2015

Answer:

The answer is #(16m^4)/n^8#.

Explanation:

#((2m)/(n^2))^4#

#((a)/(b))^x=(a^x)/(b^x)#

#(2m)^4/(n^2)^4#

#(a^x)^y=a^(x*y)#

#(2m)^4/(n^(2*4)# =

#(2m)^4/n^8#

#(ab)^x=a^xb^y#

#(2^4m^4)/n^8# =

#(16m^4)/n^8#