\({1 \over p^5}=p^{-5}\)

\({a^8 \over a^{-2}}=a^{8--2}=a^{10}\)

\(x^4⋅x^{-6}=x^{4+-6}=x^{-2}\)

\((a^2)^{-8}=a^{2⋅-8}=a^{-16}\)

\(x^2⋅{1 \over x^8}=x^2⋅x^{-8}=x^{2+-8}=x^{-6}\)

\({({1 \over a^9}) \over a^6}={a^{-9} \over a^6}=a^{-9-6}=a^{-15}\)

\({x^7 \over x^0}=x^{7-0}=x^7\)

\({6 \over p^4}\)

\({3x^2 \over 8x^3}={3 \over 8}⋅{x^2 \over x^3}={3 \over 8}⋅x^{2-3}={3 \over 8}x^{-1}\)

\({x^6 \over ({1 \over x^8})}={x^6 \over x^{-8}}=x^{6--8}=x^{14}\)

\({7a^7b^3 \over 4a^4b^7}={7 \over 4}⋅{a^7 \over a^4}⋅{b^3 \over b^7}={7 \over 4}⋅a^{7-4}⋅a^{3-7}=1\frac{3}{4}a^3b^{-4}\)

\(x^3⋅\sqrt[8]{x}=x^3⋅x^{\frac{1}{8}}=x^{3+\frac{1}{8}}=x^{3\frac{1}{8}}\)

\(p^3⋅\sqrt[4]{p^3}=p^3⋅p^{\frac{3}{4}}=p^{3+\frac{3}{4}}=p^{3\frac{3}{4}}\)

\({x^5 \over \sqrt[9]{x^7}}={x^5 \over x^{\frac{7}{9}}}=x^{5-\frac{7}{9}}=x^{4\frac{2}{9}}\)

\({1 \over a^4}⋅\sqrt[7]{a^2}=a^{-4}⋅a^{\frac{2}{7}}=a^{-4+\frac{2}{7}}=a^{-3\frac{5}{7}}\)

\({\sqrt[8]{a^7} \over \sqrt[9]{a^5}}={a^{\frac{7}{8}} \over a^{\frac{5}{9}}}=a^{\frac{7}{8}-\frac{5}{9}}=a^{\frac{23}{72}}\)

\(\sqrt[9]{{1 \over x^4}}=\sqrt[9]{x^{-4}}=x^{-\frac{4}{9}}\)

\(\sqrt[4]{p^{16}}=p^{\frac{16}{4}}=p^4\)

\({a^7 \over a^6⋅\sqrt[9]{a^5}}={a^7 \over a^6⋅a^{\frac{5}{9}}}={a^7 \over a^{6\frac{5}{9}}}=a^{7-6\frac{5}{9}}=a^{\frac{4}{9}}\)

\({4b^2 \over 7a^3}\)

\((3a)^{-2}=3^{-2}⋅a^{-2}={1 \over 3^2}⋅{1 \over a^2}={1 \over 9a^2}\)

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

\(7x^{9\frac{2}{9}}=7⋅x^9⋅x^{\frac{2}{9}}=7x^9⋅\sqrt[9]{x^2}\)

\(\frac{3}{5}a^{-\frac{2}{5}}b^{\frac{1}{5}}=\frac{3}{5}⋅{1 \over a^{\frac{2}{5}}}⋅b^{\frac{1}{5}}={3⋅\sqrt[5]{b} \over 5⋅\sqrt[5]{a^2}}\)