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

\({x^5 \over x^{-4}}=x^{5--4}=x^9\)

\(a^3⋅a^{-8}=a^{3+-8}=a^{-5}\)

\((x^4)^{-9}=x^{4⋅-9}=x^{-36}\)

\(a^2⋅{1 \over a^9}=a^2⋅a^{-9}=a^{2+-9}=a^{-7}\)

\({({1 \over p^8}) \over p^3}={p^{-8} \over p^3}=p^{-8-3}=p^{-11}\)

\({a^5 \over a^0}=a^{5-0}=a^5\)

\({2 \over x^7}\)

\({5p^5 \over 9p^{10}}={5 \over 9}⋅{p^5 \over p^{10}}={5 \over 9}⋅p^{5-10}={5 \over 9}p^{-5}\)

\({a^2 \over ({1 \over a^3})}={a^2 \over a^{-3}}=a^{2--3}=a^5\)

\({9x^2y^4 \over 8xy^5}={9 \over 8}⋅{x^2 \over x^1}⋅{y^4 \over y^5}={9 \over 8}⋅x^{2-1}⋅x^{4-5}=1\frac{1}{8}xy^{-1}\)

\(a^6⋅\sqrt[8]{a}=a^6⋅a^{\frac{1}{8}}=a^{6+\frac{1}{8}}=a^{6\frac{1}{8}}\)

\(a^6⋅\sqrt[5]{a^3}=a^6⋅a^{\frac{3}{5}}=a^{6+\frac{3}{5}}=a^{6\frac{3}{5}}\)

\({p^2 \over \sqrt[7]{p^3}}={p^2 \over p^{\frac{3}{7}}}=p^{2-\frac{3}{7}}=p^{1\frac{4}{7}}\)

\({1 \over x^8}⋅\sqrt[9]{x^5}=x^{-8}⋅x^{\frac{5}{9}}=x^{-8+\frac{5}{9}}=x^{-7\frac{4}{9}}\)

\({\sqrt[7]{x^4} \over \sqrt[7]{x^2}}={x^{\frac{4}{7}} \over x^{\frac{2}{7}}}=x^{\frac{4}{7}-\frac{2}{7}}=x^{\frac{2}{7}}\)

\(\sqrt[3]{{1 \over x^2}}=\sqrt[3]{x^{-2}}=x^{-\frac{2}{3}}\)

\(\sqrt[3]{a^9}=a^{\frac{9}{3}}=a^3\)

\({p^4 \over p^7⋅\sqrt[8]{p^7}}={p^4 \over p^7⋅p^{\frac{7}{8}}}={p^4 \over p^{7\frac{7}{8}}}=p^{4-7\frac{7}{8}}=p^{-3\frac{7}{8}}\)

\({6y^6 \over 7x^7}\)

\((2a)^{-4}=2^{-4}⋅a^{-4}={1 \over 2^4}⋅{1 \over a^4}={1 \over 16a^4}\)

\(({1 \over 4}x)^{-2}=(4^{-1}⋅x)^{-2}=(4^{-1})^{-2}⋅x^{-2}=4^2⋅x^{-2}={16 \over x^2}\)

\(2a^{4\frac{5}{9}}=2⋅a^4⋅a^{\frac{5}{9}}=2a^4⋅\sqrt[9]{a^5}\)

\(\frac{4}{5}x^{-\frac{5}{6}}y^{\frac{1}{8}}=\frac{4}{5}⋅{1 \over x^{\frac{5}{6}}}⋅y^{\frac{1}{8}}={4⋅\sqrt[8]{y} \over 5⋅\sqrt[6]{x^5}}\)