\({1 \over x^4}=x^{-4}\)

\({2a^3 \over 3a^4}={2 \over 3}⋅{a^3 \over a^4}={2 \over 3}⋅a^{3-4}={2 \over 3}a^{-1}\)

\({p^4 \over p^{-8}}=p^{4--8}=p^{12}\)

\(x^3⋅x^{-6}=x^{3+-6}=x^{-3}\)

\((a^5)^{-2}=a^{5⋅-2}=a^{-10}\)

\(a^3⋅{1 \over a^8}=a^3⋅a^{-8}=a^{3+-8}=a^{-5}\)

\({p^8 \over p^0}=p^{8-0}=p^8\)

\({8 \over a^4}\)

\((5x)^{-2}=5^{-2}⋅x^{-2}={1 \over 5^2}⋅{1 \over x^2}={1 \over 25x^2}\)

\(x^2⋅\sqrt[8]{x}=x^2⋅x^{\frac{1}{8}}=x^{2+\frac{1}{8}}=x^{2\frac{1}{8}}\)

\(a^8⋅\sqrt[8]{a^7}=a^8⋅a^{\frac{7}{8}}=a^{8+\frac{7}{8}}=a^{8\frac{7}{8}}\)

\({a^8 \over \sqrt[8]{a^5}}={a^8 \over a^{\frac{5}{8}}}=a^{8-\frac{5}{8}}=a^{7\frac{3}{8}}\)

\({1 \over p^5}⋅\sqrt[7]{p^2}=p^{-5}⋅p^{\frac{2}{7}}=p^{-5+\frac{2}{7}}=p^{-4\frac{5}{7}}\)

\({\sqrt[9]{x^7} \over \sqrt[8]{x^5}}={x^{\frac{7}{9}} \over x^{\frac{5}{8}}}=x^{\frac{7}{9}-\frac{5}{8}}=x^{\frac{11}{72}}\)

\(\sqrt{x^6}=x^{\frac{6}{2}}=x^3\)

\({p^7 \over p^5⋅\sqrt[8]{p^3}}={p^7 \over p^5⋅p^{\frac{3}{8}}}={p^7 \over p^{5\frac{3}{8}}}=p^{7-5\frac{3}{8}}=p^{1\frac{5}{8}}\)

\(2a^{9\frac{2}{9}}=2⋅a^9⋅a^{\frac{2}{9}}=2a^9⋅\sqrt[9]{a^2}\)