How do you simplify $y^{- 3} x^{5} \cdot y^{5} x^{- 3}$ $y^-3x^5*y^5x^-3$ ?

Question

2294 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:

$x^{5} \cdot x^{- 3} \cdot y^{- 3} \cdot y^{5} \Rightarrow$ $x^5 * x^-3 * y^-3 * y^5 =>$

$(x^{5} \cdot x^{- 3}) (y^{- 3} \cdot y^{5})$ $(x^5 * x^-3)(y^-3 * y^5)$

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

$z^{a} \times z^{b} = z^{a + b}$ $z^color(red)(a) xx z^color(blue)(b) = z^(color(red)(a) + color(blue)(b))$

$(x^{5} \times x^{- 3}) (y^{- 3} \times y^{5}) \Rightarrow$ $(x^color(red)(5) xx x^color(blue)(-3))(y^color(red)(-3) xx y^color(blue)(5)) =>$

$x^{5 + - 3} y^{- 3 + 5} \Rightarrow$ $x^(color(red)(5) + color(blue)(-3))y^(color(red)(-3) + color(blue)(5)) =>$

$x^{5 - 3} y^{- 3 + 5} \Rightarrow$ $x^(color(red)(5) - color(blue)(3))y^(color(red)(-3) + color(blue)(5)) =>$

$x^{2} y^{2}$ $x^2y^2$

Answer 2 · 2018-06-03T21:14:08

$x^{2} y^{2}$ $x^2y^2$

$y^{- 3} x^{5} \cdot y^{5} x^{- 3}$ $y^-3 x^5 cdot y^5 x^-3$

Collecting like terms..

$y^{- 3} \cdot y^{5} \cdot x^{5} \cdot x^{- 3}$ $y^-3 cdot y^5 cdot x^5 cdot x^-3$

$y^{- 3 + 5} \cdot x^{5 + (- 3)}$ $y^(-3 + 5) cdot x^(5 + (-3))$

$y^{2} \cdot x^{5 - 3}$ $y^2 cdot x^(5 - 3)$

$y^{2} \cdot x^{2}$ $y^2 cdot x^2$

$x^{2} y^{2}$ $x^2y^2$

How do you simplify y−3x5⋅y5x−3y^-3x^5*y^5x^-3?