# How do you simplify x^ { 2} ( p ^ { 5} ) ^ { 2} y - \frac { 3x ^ { 2} p ^ { 10} } { y ^ { - 1} } + \frac { 4x ^ { 3} p ^ { 8} } { x ^ { 2} p ^ { - 2} } - \frac { 2p ^ { 10} } { x ^ { - 1} y ^ { - 1} }?

Nov 16, 2017

${p}^{10} x \left(- 2 x y - 2 y + 4\right)$

#### Explanation:

Simplify
x^2(p^5)^2y−(3x^2p^10)/(y^(−1))+(4x^3p^8)/(x^2p^(−2))−(2p^10)/(x^(−1)y^(−1))

1) First clear the negative exponents by flipping them up to the numerator and reversing their signs to plus.
After you have flipped the negative exponents to the numerator, you will have this:
x^2(p^5)^2y−3p^10x^2y + (4x^3p^10)/x^2−2p^10xy

2) Now the only denominator is the ${x}^{2}$, which cancels with the ${x}^{3}$ in its numerator, giving you this:
x^2(p^5)^2y−3p^10x^2y + 4p^10x−2p^10xy

3) Write ${\left({p}^{5}\right)}^{2}$ in the first term as ${p}^{10}$
p^10x^2y−3p^10x^2y + 4p^10x−2p^10xy

4) Factor out ${p}^{10} x$ which is common to every term
p^10x(xy−3xy + 4−2y)

5) Combine like terms and arrange the terms in the usual order
p^10x(-2xy −2y + 4)