How do you simplify #y^-3x^5*y^5x^-3#?

Question

1923 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-03T21:13:17

See a solution process below:

First, rewrite the expression as:

#x^5 * x^-3 * y^-3 * y^5 =>#

#(x^5 * x^-3)(y^-3 * y^5)#

Next, use this rule for exponents to simplify the #x# and #y# terms:

#z^color(red)(a) xx z^color(blue)(b) = z^(color(red)(a) + color(blue)(b))#

#(x^color(red)(5) xx x^color(blue)(-3))(y^color(red)(-3) xx y^color(blue)(5)) =>#

#x^(color(red)(5) + color(blue)(-3))y^(color(red)(-3) + color(blue)(5)) =>#

#x^(color(red)(5) - color(blue)(3))y^(color(red)(-3) + color(blue)(5)) =>#

#x^2y^2#

Answer 2 · 2018-06-03T21:14:08

#x^2y^2#

#y^-3 x^5 cdot y^5 x^-3#

Collecting like terms..

#y^-3 cdot y^5 cdot x^5 cdot x^-3#

#y^(-3 + 5) cdot x^(5 + (-3))#

#y^2 cdot x^(5 - 3)#

#y^2 cdot x^2#

#x^2y^2#