The first rule you need to know is
[tex](a^b)^c=a^{bc}[/tex]
So, you have
[tex]\dfrac{(x^{25})^{-6}}{(x^{-3})^{48}}=\dfrac{x^{25\cdot(-6)}}{x^{-3\cdot 48}}=\dfrac{x^{-150}}{x^{-144}}[/tex]
The second rule you need to know is
[tex]\dfrac{a^b}{a^c}=a^{b-c}[/tex]
So, you have
[tex]\dfrac{x^{-150}}{x^{-144}}=x^{-150-(-144)}=x^{-150+144}=x^{-6}[/tex]
