Question

P^-4q^3r^-7 over p^-2q^3p^-2 simplify

Answer 1

`\bf \cfrac{p^(-4)~~\begin{matrix} q^3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ r^(-7)}{p^(-2)~~\begin{matrix} q^3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ p^(-2)}\implies \cfrac{1}{p^(4)p^(-2)p^(-2)r^7}\implies \cfrac{1}{p^(4-2-2)r^7}\implies \cfrac{1}{p^0r^7}\implies \cfrac{1}{r^7}`

Answer 2

`\large\boxed{r^(-7)=(1)/(r^7)}`

Explanation:

`(p^(-4)q^3r^(-7))/(p^(-2)q^3p^(-2))\qquad\text{use}\ (a^n)/(a^m)=a^(n-m)\\\\=p^(-4-(-2)-(-2))q^(3-3)r^(-7)\\\\=p^(-4+2+2)q^0r^(-7)\\\\=p^0q^0r^(-7)\\\\=r^(-7)\qquad\text{use}\ a^(-n)=(1)/(a^n)\\\\=(1)/(r^7)`