Question

Simplify and express with a positive index.

`((27y^9)/(64x^6))^(2/3)`

Answer 1

Given,

`((27y^9)/(64x^6))^(2/3)`

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

Thus, `((27y^9)/(64x^6))^(2/3)`

⇒ `(27y^9)^(2/3)/(64x^6)^(2/3)`    ...`[∴ (a/b)^n = a^n/b^n]`

⇒ `[((3^3)^(2/3) xx (y^9)^(2/3))/((4^3)^(2/3) xx (x^6)^(2/3))]`  ...[∴ (ab)ⁿ = aⁿ × bⁿ]

⇒ `[((3)^(3 xx 2/3) xx (y)^(9 xx 2/3))/((4)^(3 xx 2/3) xx (x)^(6 xx 2/3))]`

⇒ `(3^2 xx y^6)/(4^2 xx x^4)`   ...[∴ (aⁿ)^m = a^nm]

⇒ `(9y^6)/(16x^4)`

Hence, `((27y^9)/(64x^6))^(2/3) = (9y^6)/(16x^4)`.