Question

Find the value of `(27/8)^(2/3) - 7^0 + (1/4)^-2`

Answer 1

Given,

`(27/8)^(2/3) - 7^0 + (1/4)^-2`

We need to simplify the given terms.

Thus, `(27/8)^(2/3) - 7^0 + (1/4)^-2`

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

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

⇒ `(3/2)^2 - 1 + 4^2` 

⇒ `9/4 - 1 + 16`

⇒ `(9 - 4 + 64)/4`

= `(73 - 4)/4` 

= `69/4`

⇒ `17 1/4`

Hence, `(27/8)^(2/3) - 7^0 + (1/4)^-2 = 17 1/4`.