Question

Can someone please help me on this problem? I think I was doing it wrong...

Answer 1

x^(-1/12)y^(-19/8)

Explanation:

There are three rules of exponents that apply here:

(a^b)(a^c) = a^(b+c)

(a^b)^c = a^(b·c)

1/a^b = a^-b

Using these rules the expression simplifies as ...

`\displaystyle\frac{x^{(1)/(2)}y^{-(5)/(4)}\left(x^{(1)/(6)}y^{-(1)/(4)}\right)^{(1)/(2)}}{x^{(2)/(3)}y^(1)}=x^{(1)/(2)+(1)/(6)\cdot(1)/(2)-(2)/(3)}y^{-(5)/(4)-(1)/(4)\cdot(1)/(2)-1}=x^{-(1)/(12)}y^{-(19)/(8)}`

So, the simplified expression is ...

x^(-1/12)y^(-19/8)