Simplify the Expression.Eliminate any negative exponents.Assume all variables are positve number. ?

Question

(x to the -10 power y^4 z^5)negative 2/7

Answer 1

I'm going to use ^ to denote the exponent.  So x to the fifth power is x^5 and y to the negative 4 is y^(-4).  I'm not sure I understand your question but I believe you are trying to solve

(x^(-10)y^4z^5)^(-2/7)

When you have a base with a negative exponent you move the base to the other side of the fraction and make the exponent positive.  For instance, x^(-6) = 1/x^6 and 1/y^(-7) = y^7.  In your case start with the outermost parentheses,

(x^(-10)y^4z^5)^(-2/7) =

1 / (x^(-10)y^4z^5)^(2/7) =

1 / ((x^(-10))^(2/7)(y^4)^(2/7)(z^5)^(2/7)) =

When you raise an exponent to another exponent you multiply them together.  So, (a^b)^c = a^(bc).  In your case,

1 / ((x^(-10))^(2/7)(y^4)^(2/7)(z^5)^(2/7)) =

1 / (x^(-10*2/7)y^(4*2/7)z^(5*2/7)) =

1 / (x^(-20/7)y^(8/7)z^(10/7)) =

x^(20/7) / (y^(8/7)z^(10/7))

Hope this helps you!