Question

Which expression is equivalent to StartFraction RootIndex 7 StartRoot x squared EndRoot Over RootIndex 5 StartRoot y cubed EndRoot? Assume y not-equals 0.
(x Superscript two-sevenths Baseline) (y Superscript negative three-fifths Baseline)
(x Superscript two-sevenths Baseline) (y Superscript five-thirds Baseline)
(x Superscript two-sevenths Baseline) (y Superscript three-fifths Baseline)
(x Superscript seven-halves Baseline) (y Superscript negative five-thirds Baseline)

Answer 1

Convert roots to rational exponents: 7th root of x^2 = x^(2/7), 5th root of y^3 = y^(3/5). So

(7th root of x^2)/(5th root of y^3) = x^(2/7)/y^(3/5) = x^(2/7) y^(-3/5).

Answer: (x^(2/7))(y^(-3/5)).