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

1 Answer
Jan 26, 2018

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#