Question

Find the value of `9^(3/2) - 3(5)^0 - (1/81)^((-1)/2)`

Answer 1

Given,

`9^(3/2) - 3(5)^0 - (1/81)^((-1)/2)`

We need to simplify the given terms.

Thus, `9^(3/2) - 3(5)^0 - (1/81)^((-1)/2)`  ...[∴ a⁰ = 1 where a ≠ 0]

⇒ `(3^2)^(3/2) - 3 xx 1 - (1/9^2)^((-1)/2)`  ...[∴ (a^m)ⁿ = a^mn]

⇒ `(3)^(2 xx 3/2) - 3 - (9^-2)^((-1)/2)`  ...`[∴ a^-n = 1/a^n]`

⇒ (3)³ – 3 – 9

⇒ 27 – 12

= 15

Hence, `9^(3/2) - 3(5)^0 - (1/81)^((-1)/2) = 15`.