Question

Calculate:

`3^(5/3) xx 2^((-1)/3) xx 36^(2/3)`

Answer 1

Given,

`3^(5/3) xx 2^((-1)/3) xx 36^(2/3)`

We need to simplify the given terms.

Thus, `3^(5/3) xx 2^((-1)/3) xx 36^(2/3)`

⇒ `3^(5/3) xx 2^((-1)/3) xx (6^2)^(2/3)`

⇒ `3^((6/3 + (-1)/3)) xx 2^((-1)/3) xx (6)^(2 xx 2/3)`

⇒  `3^(6/3) xx 3^((-1)/3) xx 2^((-1)/3) xx 6^(4/3)`...[∴ (a^m)ⁿ = a^mn]

⇒ `3^2 xx (3 xx 2)^((-1)/3) xx (6)^(4/3)`  ...[∴ aⁿ × bⁿ = (ab)ⁿ]

⇒ `3^2 xx (6)^((-1)/3) xx (6)^(4/3)`

⇒ `3^2 xx (6)^((-1)/3 + 4/3)`   ...[∴ aⁿ × a^m = a^{n + m}]

⇒ 9 × 6 = 54

Hence, the required is 54.