Question

How do you simplify `((x^-3 y^-4 )/ (x^-5 y^-7 )) ^-3`?

Answer 1

See a solution process below:

Explanation:

First, use this rule of exponents to divide the `x` and `y` terms within the parenthesis:

`x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))`

`((x^color(red)(-3)y^color(red)(-4))/(x^color(blue)(-5)y^color(blue)(-7)))^-3 =>`

`(x^(color(red)(-3)-color(blue)(-5))y^(color(red)(-4)-color(blue)(-7)))^-3 =>`

`(x^(color(red)(-3)+color(blue)(5))y^(color(red)(-4)+color(blue)(7)))^-3 =>`

`(x^color(red)(2)y^color(red)(3))^color(blue)(-3)`

Next, use this rule for exponents to eliminate the outer exponent:

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

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

`x^color(red)(-6)y^color(red)(-9)`

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

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

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

`1/(x^color(red)(6)y^color(red)(9))`