Question

How do you simplify `[(-2x y ^ { 2} ) ^ { 3} ] ^ { 2}`?

Answer 1

See a solution process below:

Explanation:

First, use this rule of exponents to eliminate the outer brackets:

`(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))`

`[(-2xy^2)^color(red)(3)]^color(blue)(2) => (-2xy^2)^(color(red)(3)xxcolor(blue)(2)) => (-2xy^2)^6`

Next, use this rule of exponents to rewrite the term inside the parenthesis:

`a^color(red)(1) = a` or `a = a^color(red)(1)`

`(-2xy^2)^6 => (-2^color(red)(1)x^color(red)(1)y^2)^6`

Now, use the rule in the first step again to eliminate the parenthesis and complete the simplification:

`(-2^color(red)(1)x^color(red)(1)y^color(red)(2))^color(blue)(6) => -2^(color(red)(1)xx^color(blue)(6))x^(color(red)(1)xx^color(blue)(6))y^(color(red)(2)xx^color(blue)(6)) => -2^6x^6y^12 =>`

`64x^6y^12`