3squareroot 3t4 v2 3squareroot 9tv5Solution33t4v2 39tv5 3t4

Solution

³(3t⁴v²) ³(-9tv⁵)

= (3t⁴v²)^1/3 (-9tv⁵)^1/3       since ⁿa = a^1/n

= (3)^1/3(t⁴)^1/3(v²)^1/3(-1)(3²)^1/3(t)^1/3(v⁵)^1/3 since (ab)ⁿ = aⁿbⁿ

= -(3^1/3)(t^4/3)(v^2/3)(3^2/3)(t^1/3)(v^5/3)       since (a^m)ⁿ = a^mn

= -(3^{1/3 + 2/3})(t^{4/3 + 1/3})(v^{2/3 + 5/3})   since a^m aⁿ = a^m+n

= -3t^5/3v^7/3

==> ³(3t⁴v²) ³(-9tv⁵) = -3t^5/3v^7/3