How do you simplify (3x^7y^3)^4/(12xy^3)(3x7y3)412xy3?

1 Answer
Jun 12, 2015

color(blue)(27/4x^27.y^9274x27.y9

Explanation:

(3x^7y^3)^4/(12xy^3)(3x7y3)412xy3

(3x^7y^3)^color(red)(4) = 3^color(red)(4).x^(7 . color(red)(4)). y^(3 .color(red)(4)(3x7y3)4=34.x7.4.y3.4

= 3^4x^28y^12=34x28y12

now the expression can be re written as :
(3^4x^28y^12)/(12xy^3)34x28y1212xy3

Note :
color(blue)(a^m . a^n = a^(m+n)am.an=am+n
color(blue)(a^m/a^ n=a^(m-n)aman=amn

Applying the above to the exponents of xx and yy

= (81/12) . x^(28-1) . y^(12-3=(8112).x281.y123
= color(blue)(27/4x^27.y^9=274x27.y9