How do you simplify ((2m)/ n^2)^4(2mn2)4?

2 Answers
Jul 13, 2015

((2m)/n^2)^4 = (16m^4)/n^8(2mn2)4=16m4n8

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

((2m)/n^2)^4 = (2^4m^4)/(n^2)^4(2mn2)4=24m4(n2)4

We have to repeat the procedure with the denominator.

(2^4m^4)/(n^2)^4 = (2^4m^4)/n^824m4(n2)4=24m4n8

So

((2m)/n^2)^4 = (2^4m^4)/n^8=(16m^4)/n^8(2mn2)4=24m4n8=16m4n8

Jul 13, 2015

The answer is (16m^4)/n^816m4n8.

Explanation:

((2m)/(n^2))^4(2mn2)4

((a)/(b))^x=(a^x)/(b^x)(ab)x=axbx

(2m)^4/(n^2)^4(2m)4(n2)4

(a^x)^y=a^(x*y)(ax)y=axy

(2m)^4/(n^(2*4)(2m)4n24 =

(2m)^4/n^8(2m)4n8

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

(2^4m^4)/n^824m4n8 =

(16m^4)/n^816m4n8