Question

Leave answer in the simplest radical form.


`(7x^-^3^/^2y^5^/^2z^-^2^/^3)/(56x^-^1^/^2y^1^/^4)`

Answer 1

`\cfrac{7x^{-(3)/(2)} ~~ y^{(5)/(2)} ~~ z^{-(2)/(3)}}{56 x^{-(1)/(2)} ~~ y^{(1)/(4)}}\implies \cfrac{7}{56}\cdot \cfrac{y^{(5)/(2)} ~~ y^{-(1)/(4)}}{x^{-(1)/(2)} ~~ x^{(3)/(2)} ~~ z^{(2)/(3)}}\implies \cfrac{1}{8}\cfrac{y^{(5)/(2)-(1)/(4)}}{x^{-(1)/(2)+(3)/(2)}~~ z^{(2)/(3)}}`

`\cfrac{y^{(9)/(4)}}{8x z^{(2)/(3)}}\implies \cfrac{\sqrt[4]{y^9}}{8x\sqrt[3]{z^2}}\implies \cfrac{\sqrt[4]{y (y^2)^4}}{8x\sqrt[3]{z^2}}\implies \cfrac{y^2 \sqrt[4]{y}}{8x\sqrt[3]{z^2}}`