properties of radicals

Question

Using properties of radicals Simplify the expression. 1)(5)1/3×(25)1/3 2)(3)1/4×(27)1/4 3)(64)1/2×(4)1/2 4)(256)1/3×(4)1/3 5)(16)1/3×(2)1/3

 

Answer 1

1) (5)^1/3×(25)^1/3

 =(5)^1/3×(5^2)^1/3

=(5)^1/3×(5^1/3)^2

=(5)^1/3[A-5^1/3]

2)(3)^1/4×(27)^1/4

⁼(3)^1/4×(3^3)^1/4

=(3)^1/4×(3^{1/4)^3}

⁼(3)^1/4[×3^2/4]

3)(64)^1/2×(4)^1/2

⁼(4^3)^1/2×(4)^1/2

⁼(4^{1/2)^3}×(4)^1/2

=4^1/2[(4)^2/2×1]

4)(256)^1/3×(4)^1/3

=(4^4)^1/3×(4)^1/3

=(4^{1/3) ^4}×(4)^1/3

=(4)^1/3[(4)^3/3×1]

5)(16)^1/3×(2)^1/3

=(2^4)^1/3×(2)^1/3

⁼(2^{1/3) ^4}×(2)^1/3

=(2)^1/3[(2)^3/3×1]