Perform the indicated operation and express the answer in si

Perform the indicated operation and express the answer in simplest form.

Solution

((4(a^2)b)^(1/3))×((2(a^4)b)^(1/3))

We know that x^n × y^n = (xy)^n

So we can write given expression as

=> ((4(a^2)b)×(2(a^4)b))^(1/3)

=> (8(a^6)(b^2))^(1/3)

=> ((2^3)^(1/3)) × (((a^2)^3)^(1/3)) × ((b^2)^(1/3)

=> 2 × (a^2) × ((b^(1/3))^2)

=> 2(a(b)^(1/3))^2 this is simplified form for the given expression.