Express each of the following as a rational number:
( i ) `5^(-3)` ( ii ) `(-2)^(-5)`
( iii ) `(frac(1)(4))^(-4)`
( iv ) `(frac(-3)(4))^(-3)`
( v ) `(-3)^(-1) xx (frac(1)(3))^(-1)`
( vi ) `(frac(5)(7))^(-1) xx (frac(7)(4))^(-1)`
( vii ) `(5^(-1)-7^(-1))^(-1)`
( viii ) `{(frac(4)(3))^(-1)-(frac(1)(4))^(-1)}^(-1)`
( ix ) `{(frac(3)(2))^(-1) div (frac(-2)(5))^(-1)}`
( x ) `(frac(23)(25))^(@)`

Answer

(i) `frac(1)(125)`
(ii) `frac(-1)(32)`
(iii) 256
(iv) `frac(-64)(27)`
(v) -1
(vi) `frac(4)(5)`
(vii) `frac(35)(2)`
(viii) `frac(-4)(13)`
(ix) `frac(-4)(15)`
(x) 1