Simplify the following algebraic expressions as directed 24

Simplify the following algebraic expressions, as directed. [ 24 x^-4 y^2/3 x^-7 y^8]^ 1/3, and express your answer using positive exponents only.

Solution

[(24x^-4y²) /(3x^-7y⁸)]^1/3

= [(24/3)(x^-4/x^-7)(y²/y⁸)]^1/3

= [8(1/x^-3)(1/y⁶)]^1/3

= [8x³/y⁶]^1/3

= 2x/y²