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

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

\(a^4⋅a^{-7}=a^{4+-7}=a^{-3}\)

\((a^8)^{-5}=a^{8⋅-5}=a^{-40}\)

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

\({({1 \over a^9}) \over a^4}={a^{-9} \over a^4}=a^{-9-4}=a^{-13}\)

\({x^0 \over x^9}=x^{0-9}=x^{-9}\)

\({5 \over p^6}\)

\({5x \over 8x^3}={5 \over 8}⋅{x \over x^3}={5 \over 8}⋅x^{1-3}={5 \over 8}x^{-2}\)

\({x^2 \over ({1 \over x^5})}={x^2 \over x^{-5}}=x^{2--5}=x^7\)

\({5a^6b^4 \over 4a^2b^5}={5 \over 4}⋅{a^6 \over a^2}⋅{b^4 \over b^5}={5 \over 4}⋅a^{6-2}⋅a^{4-5}=1\frac{1}{4}a^4b^{-1}\)

\(x^3⋅\sqrt[6]{x}=x^3⋅x^{\frac{1}{6}}=x^{3+\frac{1}{6}}=x^{3\frac{1}{6}}\)

\(x^6⋅\sqrt[3]{x^2}=x^6⋅x^{\frac{2}{3}}=x^{6+\frac{2}{3}}=x^{6\frac{2}{3}}\)

\({a^2 \over \sqrt[7]{a^6}}={a^2 \over a^{\frac{6}{7}}}=a^{2-\frac{6}{7}}=a^{1\frac{1}{7}}\)

\({1 \over p^7}⋅\sqrt[8]{p^3}=p^{-7}⋅p^{\frac{3}{8}}=p^{-7+\frac{3}{8}}=p^{-6\frac{5}{8}}\)

\({\sqrt[9]{x^7} \over \sqrt[7]{x^2}}={x^{\frac{7}{9}} \over x^{\frac{2}{7}}}=x^{\frac{7}{9}-\frac{2}{7}}=x^{\frac{31}{63}}\)

\(\sqrt[5]{{1 \over a^4}}=\sqrt[5]{a^{-4}}=a^{-\frac{4}{5}}\)

\(\sqrt[3]{p^{12}}=p^{\frac{12}{3}}=p^4\)

\({x^2 \over x^7⋅\sqrt[3]{x^2}}={x^2 \over x^7⋅x^{\frac{2}{3}}}={x^2 \over x^{7\frac{2}{3}}}=x^{2-7\frac{2}{3}}=x^{-5\frac{2}{3}}\)

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

\((5p)^{-4}=5^{-4}⋅p^{-4}={1 \over 5^4}⋅{1 \over p^4}={1 \over 625p^4}\)

\(({1 \over 3}a)^{-5}=(3^{-1}⋅a)^{-5}=(3^{-1})^{-5}⋅a^{-5}=3^5⋅a^{-5}={243 \over a^5}\)

\(3a^{8\frac{2}{3}}=3⋅a^8⋅a^{\frac{2}{3}}=3a^8⋅\sqrt[3]{a^2}\)

\(\frac{1}{8}a^{-\frac{7}{8}}b^{\frac{1}{2}}=\frac{1}{8}⋅{1 \over a^{\frac{7}{8}}}⋅b^{\frac{1}{2}}={1⋅\sqrt{b} \over 8⋅\sqrt[8]{a^7}}\)