Question

Evaluate:

`[343^(1/3) + 8^(2/3) xx 125^(1/3)]^(1/3)`

Answer 1

Given,

`[343^(1/3) + 8^(2/3) xx 125^(1/3)]^(1/3)`

We have to evaluate the given terms.

Thus, `[343^(1/3) + 8^(2/3) xx 125^(1/3)]^(1/3)`

⇒ `[(7^3)^(1/3) + (2^3)^(2/3) xx (5^3)^(1/3)]^(1/3)`  ...[(a^m)ⁿ = a^mn]

⇒ `[(7)^(3 xx 1/3) + (2)^(3 xx 2/3) xx (5)^(3 xx 1/3)]^(1/3)`

⇒ `[7 + 2^2 xx 5]^(1/3)`

⇒ `[7 + 20]^(1/3)`

⇒ `[27]^(1/3) = (3^3)^(1/3) = 3`

Hence, `[343^(1/3) + 8^(2/3) xx 125^(1/3)]^(1/3) = 3`