Question

Find the value of `16^(3/4) + 2(1/2)^-1 - 3^0 + (0.027)^((-2)/3`

Answer 1

Given,

`16^(3/4) + 2(1/2)^-1 - 3^0 + (0.027)^((-2)/3`

We need to simplify the given terms.

Thus, `16^(3/4) + 2(1/2)^-1 - 3^0 + (0.027)^((-2)/3` ...[∴ a⁰ = 1 where a ≠ 0]

⇒ `(2^4)^(3/4) + 2(2^-1)^(-1) - 1 + (27/1000)^((-2)/3)`  ...`[∴ a^-n = 1/a^n]`

⇒ `(2)^(4 xx 3/4) + (2 xx 2) - 1 + (3^3/10^3)^((-2)/3)`  ...[∴ (a^m)ⁿ = a^mn]

⇒ `(2)^3 + 4 - 1 + (3/10)^(3 xx (-2)/3)`

⇒ `8 + 4 - 1 + (3/10)^-2`

⇒ `8 + 4 - 1 + (10/3)^2`  ...`[∴ (a/b)^-n = (b/a)^n]`

⇒ `12 - 1 + 100/9`

⇒ `(108 - 9 + 100)/9`

= `(208 - 9)/9`

= `199/9`

= `22 1/9`

Hence, `16^(3/4) + 2(1/2)^-1 - 3^0 + (0.027)^((-2)/3) = 22 1/9`.