Question

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

Answer 1

See a solution process below:

Explanation:

First, use this rule of exponents to rewrite the term within the parenthesis;

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

`(-2x^-3y^2)^3 => (-2^color(red)(1)x^-3y^2)^3`

Next, use this rule of exponents to eliminate the parenthesis:

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

`(-2^color(red)(1)x^color(red)(-3)y^color(red)(2))^color(blue)(3) => -2^(color(red)(1)xxcolor(blue)(3))x^(color(red)(-3)xxcolor(blue)(3))y^(color(red)(2)xxcolor(blue)(3)) => -2^3x^-9y^6 => -8^3x^-9y^6`

Now, use this rule of exponents to eliminate the negative exponent:

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

`-8^3x^color(red)(-9)y^6 => -8^3(1/x^color(red)(- -9))y^6 => -8^3(1/x^color(red)(9))y^6 => -(8^3y^6)/x^9`