Question

Simplify
(5x^7y^3z^-1)^2x(2xy^-5)^3x(2y^-3z^2)^3

Answer 1

remember

`(abc)^x=(a^x)(b^x)(c^x)`
and

`(x^m)(x^n)=x^(m+n)`
and

`(x^m)^n=x^(mn)`
and

`x^(-m)= (1)/(x^m)`
so


`(5x^7y^3z^(-1))^2(2xy^(-5))^3(2y^(-3)z^2)^3`=

`(5^2)((x^7)^2)((y^3)^2)((z^(-1))^2)(2^3)(x^3)((y^(-5))^3)(2^3)((y^(-3))^3)((z^2)^3)`=

`(25)(x^(14))(y^6)(z^(-2))(8)(x^3)(y^(-15))(8)(y^(-9))(z^6)`=

`1600x^(17)y^(-18)z^4`=

`(1600x^(17)z^4)/(y^(18))`