Question

Simplify [((0.5)^(2)*x^(3)*y^(-1))/(9^(2)-z^(-2))]^(-3)*((27x^(3))/(8y-3z^(-2)))^(-2) =

Answer 1

Simplify

$$\begin{array}{l} \left[ \frac {(0 . 5) ^ {2} * x ^ {3} * y ^ {- 1}}{9 ^ {2} - z ^ {- 2}} \right] ^ {- 3} * \left(\frac {2 7 x ^ {3}}{8 y - 3 z ^ {- 2}}\right) ^ {- 2} = \left[ \frac {3 ^ {4} - z ^ {- 2}}{2 ^ {- 2} * x ^ {3} * y ^ {- 1}} \right] ^ {3} * \left(\frac {8 y - 3 z ^ {- 2}}{(3 x) ^ {3}}\right) ^ {2} \\ = \frac {\left(\left(3 ^ {4} - z ^ {- 2}\right) * y * 2 ^ {2}\right) ^ {3}}{x ^ {9}} * \left(\frac {8 y - 3 z ^ {- 2}}{(3 x) ^ {3}}\right) ^ {2} \\ = \frac {\left(3 ^ {4} - z ^ {- 2}\right) ^ {3} * \left(8 y - 3 z ^ {- 2}\right) ^ {2} * 2 ^ {6} * y ^ {3}}{3 ^ {6} * x ^ {1 5}} \\ = \frac {\left(3 ^ {4} * z ^ {2} - 1\right) ^ {3} * \left(8 y z ^ {2} - 3\right) ^ {2} * 2 ^ {6} * y ^ {3}}{3 ^ {6} * x ^ {1 5} * z ^ {1 0}} = \frac {6 4 y ^ {3} (8 1 z ^ {2} - 1) ^ {3} (8 y z ^ {2} - 3) ^ {2}}{7 2 9 x ^ {1 5} z ^ {1 0}} \\ \end{array}$$

Answer: $\frac{64y^3(81z^2 - 1)^3(8yz^2 - 3)^2}{729x^{15}z^{10}}$