Question

What is(y^4/3 x y^2/3)^-1/2

Answer 1

Explanation:

`\text{Use}\\\\a^n\cdot a^m=a^(n+m)\\\\(a^n)^m=a^(nm)\\\\a^(-1)=(1)/(a)\\============================\\\\\bigg(y^(4)/(3)\cdot y^(2)/(3)\bigg)^{-(1)/(2)}=\bigg(y^{(4)/(3)+(2)/(3)}\bigg)^{-(1)/(2)}=\bigg(y^{(4+2)/(3)}\bigg)^{-(1)/(2)}\\\\=\bigg(y^{(6)/(3)}\bigg)^{-(1)/(2)}=\bigg(y^2\bigg)^{-(1)/(2)}=y^{(2)\left(-(1)/(2)\right)}=y^(-1)=(1)/(y)`

Answer 2

`\bf \left( y^{(4)/(3)}xy^{(2)/(3)} \right)^{-(1)/(2)}\implies \left( y^{(4)/(3)}y^{(2)/(3)}x \right)^{-(1)/(2)}\implies \left( y^{(4)/(3)+(2)/(3)}x \right)^{-(1)/(2)}\implies \left( y^{(6)/(3)}x \right)^{-(1)/(2)} \\\\\\ (y^2x^1)^{-(1)/(2)}\implies \left( y^{-(1)/(2)\cdot 2}x^{-(1)/(2)\cdot 1} \right)\implies y^(-1)x^{-(1)/(2)}\implies \cfrac{1}{y}\cdot \cfrac{1}{x^{(1)/(2)}}\implies \cfrac{1}{y√(x)}`