Question

Simplify and express with a positive index.

`(3x^-2)^3 (x^9)^(2/3)`

Answer 1

Given,

`(3x^-2)^3 (x^9)^(2/3)`

We need to simplify and express with a positive index the given terms.

We know that if x is any non-zero integer and m and n are the whole numbers.

Thus, `(3x^-2)^3 (x^9)^(2/3)`

⇒ `3^3 xx (x^-2)^3 xx (x^9)^(2/3)`  ...[∴ (ab)ⁿ = aⁿ × bⁿ]

⇒ `3^3 xx (x)^(-2 xx 3) xx x^(9 xx 2/3)`  ...[∴ (aⁿ)^m = a^nm]

⇒ `3^3 xx (x)^-6 xx (x)^6`

⇒ `3^3 xx x^6/x^6`  ...`[∴ a^-n = 1/a^n]`

⇒ `27 xx 1 = 27`

Hence, `(3x^-2)^3 (x^9)^(2/3) = 27`.