Question

Find the value of `sqrt(9/16) + (0.008)^((-2)/3) - (7/10)^0`

Answer 1

Given,

`sqrt(9/16) + (0.008)^((-2)/3) - (7/10)^0`

We need to simplify the given terms.

Thus, `sqrt(9/16) + (0.008)^((-2)/3) - (7/10)^0`

⇒ `sqrt(3^2/4^2) + (8/1000)^((-2)/3) - 1`  ...[∴ a⁰ = 1 where a ≠ 0]

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

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

⇒ `(3/4) + (2/10)^-2 - 1`

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

⇒ `(3/4) + (100/4) - 1`

⇒ `(3 + 100 - 4)/4`

⇒ `(103 - 4)/4 = 99/4 = 24 3/4`

Hence, `sqrt(9/16) + (0.008)^((-2)/3) - (7/10)^0 = 24 3/4`.