❶ Note: 5³=125, so 500=5³×4.
(5×4^⅓)(x^4/3)(y^7/3)=
(5×4^⅓)(x×x^⅓)(y²×y^⅓)=5xy²(∛(4xy)).
❷ Note: 2⁴=16, so 32=2⁴×2.
(2×2^¼)(x^¾)(y^¼)=2(⁴√(2x³y)).
❸ (4×2^½)(u^3/2)(v)=
(4×2^½)(u×u^½)(v)=4uv√(2u).
❹ 4(2^-½)(x^-½)=
4(2^(½-1))(x^(½-1))=4(2^½)/2 × (x^½)/x=
2√(2x)/x.
❺ 2n²/√(2n²)=√(2n²)=n√2.
❻ (2^(2-4/3))(n^(1-⅓))=
(2^⅔)(n^⅔)=∛(4n²).