Simplify the following quotient. 8m5n6√2m3n2√⋅6m4n4√2m3n2√ (1 point) Responses 2mn33m−−−√ 2 m n cubed square root of 3 m 48mn3n−−√ 48 m n square root of 3 n 6mn3n√3 the fraction with numerator 6 m n square root of 3 n and denominator 3 2mn3n√3
To simplify the given quotient, use the properties of radicals and multiplication:
8m^5n^6√2m^3n^2√ ÷ 6m^4n^4√2m^3n^2√
= (8/6) * (m^5/m^4) * (n^6/n^4) * √(2√2)
= (4/3) * m^(5-4) * n^(6-4) * √(2√2)
= (4/3) * m^1 * n^2 * √(2√2)
= (4/3) * m * n^2 * √(2√2)
= (4m/3) * n^2 * √(2√2)
Therefore, the simplified quotient is (4m/3) * n^2 * √(2√2).