Question

Simplify the following expression

(x^0 y^2/3 z^-2)^3/2 divided by (x^2z^1/2)^-6

Answer 1

`(\left(x^0 y^(\tfrac 23) z^(-2) \right)^(\tfrac 32))/(\left(x^2 z^(\tfrac 12) \right)^(-6))\\\\\\=(1\cdot \left( y^(\tfrac 23)\right)^(\tfrac 32) \cdot \left(z^(-2) \right)^(\tfrac 32))/(\left(x^2 \right)^(-6) \cdot \left( z^(\tfrac 12) \right)^(-6))~~~~~~~~~~~~~~~~~~;\left[(ab)^m = a^m b^m\right]\\\\\\=(y^(1) \cdot z^(-3))/(x^(-12) \cdot z^(-3))~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~;\left[(a^m)^n = a^(mn)\right]\\\\\\=(y)/(x^(-12))\\\\\\`

`=\frac{y}{\tfrac 1{x^(12)}}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~;\left[a^(-m) = \frac 1{a^m} } \right]\\\\\\=yx^(12)`