Question

How do you simplify `( 3a b ^ { 2} ) ^ { - 3}`?

Answer 1

See a solution process below:

Explanation:

Use these two rules of exponents to simplify the expression:

`a = a^color(red)(1)` and `(x^color(red)(a))^color(blue)(b) = x^(color(red)(a)xxcolor(blue)(b))`

`(3ab^2)^-3 => (3^color(red)(1)a^color(red)(1)b^color(red)(2))^color(blue)(-3) => 3^(color(red)(1)xxcolor(blue)(-3))a^(color(red)(1)xxcolor(blue)(-3))b^(color(red)(2)xxcolor(blue)(-3)) =>`

`3^-3a^-3b^-6`

Now, use this rule of exponents to complete the simplification by eliminating the negative exponent:

`x^color(red)(a) = 1/x^color(red)(-a)`

#3^color(red)(-3)a^color(red)(-3)b^color(red)(-6) => 1/(3^color(red)(- -3)a^color(red)(- -3)b^color(red)(- -6)) => 1/(3^3a^3b^6) =>#

`1/(27a^3b^6)`