Question

Simplify the expression using only positive exponents in the result. See attached pic for problem

Answer 1

In order to simplify this expression, we can use the following properties:

`\begin{gathered} (a^b)/(a^c)=a^(b-c) \\ (a^b)^c=a^(b\cdot c) \end{gathered}`

So we have:

`\begin{gathered} ((2x^(3/4)y^(-6)z^7)/(3x^4y^(-5/2)z^(-1/2)))^(-4) \\ =\frac{x^((3/4)\cdot(-4))y^((-6)\cdot(-4))z^(7\cdot(-4))}{3^(-4)x^(4\cdot(-4))y^((-5/2)\cdot(-4))z^{(-1/2)(-4)_{}}} \\ =(x^(-3)y^(24)z^(-28))/(3^(-4)x^(-16)y^(10)z^2) \\ =3^4x^(-3-(-16))y^(24-10)z^(-28-2) \\ =81x^(13)y^(14)z^(-30) \\ =(81x^(13)y^(14))/(z^(30)) \end{gathered}`