Question

Assuming that `x , y` are positive real numbers, simplify each of the following: (i) `sqrt(x^(-2)y^3)` (ii) `(x^(-2)doty^(-1/2))^2` (iii)`(sqrt(x^(-3)))^5`

Answer 1

1)`(sqrt(x^(-2)y^3))^(1/2)`
`=x^(-2/2)*y^(3/2)`
`=y^(3/2)/x`
`=(sqrty)^3/x`
2)`(x^(-2)*y^(-1/2))^2`
`=(x^((-2)*2)*y^((-1/2)*(2)))`
`=1/(ysqrtx^2)`
3)`(sqrtx^(-3))^5`
`(x^(-3+2))^5`
`x^(5-1)`
`x^4`.