Question

Simplify the expression. Write your answer without negative exponents. Assume that the variables represent nonzero real numbers

Answer 1

The rational expression
`((xy^(-2)z^(-4))/(x^2y^(-3)z^(-5)))^3`when simplified has a value of
`(y^3z^3)/(x^3)`

How to simplify the rational expression

From the question, we have the following parameters that can be used in our computation:

`((xy^(-2)z^(-4))/(x^2y^(-3)z^(-5)))^3`

Applying the law of indices, we have

`((xy^(-2)z^(-4))/(x^2y^(-3)z^(-5)))^3 = ((y^(3-2)z^(5-4))/(x^(2-1)))^3`

This gives

`((xy^(-2)z^(-4))/(x^2y^(-3)z^(-5)))^3 = ((yz)/(x))^3`

When the brackets are opened, we have

`((xy^(-2)z^(-4))/(x^2y^(-3)z^(-5)))^3 = (y^3z^3)/(x^3)`

Hence, the rational expression when simplified it
`((xy^(-2)z^(-4))/(x^2y^(-3)z^(-5)))^3 = (y^3z^3)/(x^3)`

Answer 2

Answer is in the attachment below. Open it up in a new window to see it in full.