Question

Simplify:

`(0.027a^9b^-6)^((-2)/3)`

Answer 1

We are given:

`(0.027a^9b^-6)^(-2/3)`

Step 1: Convert decimal to fraction

`0.027 = 27/1000`

= `(3^3/10^3)`

= `(3/10)^3`

So, `(0.027a^9b^-6) = ((3/10)^3 a^9b^-6)`

Step 2: Apply the exponent `-2/3`

`[(3/10)^3 a^9b^-6]^(-2/3) = (3/10)^-2 * a^-6 * b^4`

Explanation:

`[[(3/10)^3]^(-2/3) = (3/10)^-2]`

`a^(9*(-2//3)) = a^-6`

`b^(-6*(-2//3)) = b^4`

Step 3: Simplify

`(3/10)^-2 = (10/3)^2 = 100/9`

So the expression becomes:

`100/9 * a^-6 * b^4 = (100b^4)/(9a^6)`