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

\({p^4 \over p^{-3}}=p^{4--3}=p^7\)

\(x^3⋅x^{-9}=x^{3+-9}=x^{-6}\)

\((a^4)^{-2}=a^{4⋅-2}=a^{-8}\)

\(a^5⋅{1 \over a^6}=a^5⋅a^{-6}=a^{5+-6}=a^{-1}\)

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

\({a^0 \over a^2}=a^{0-2}=a^{-2}\)

\({5 \over a^9}\)

\({4x^3 \over 9x^8}={4 \over 9}⋅{x^3 \over x^8}={4 \over 9}⋅x^{3-8}={4 \over 9}x^{-5}\)

\({x^4 \over ({1 \over x^6})}={x^4 \over x^{-6}}=x^{4--6}=x^{10}\)

\({5p^2q^3 \over 3pq^5}={5 \over 3}⋅{p^2 \over p^1}⋅{q^3 \over q^5}={5 \over 3}⋅p^{2-1}⋅p^{3-5}=1\frac{2}{3}pq^{-2}\)

\(a^8⋅\sqrt[7]{a}=a^8⋅a^{\frac{1}{7}}=a^{8+\frac{1}{7}}=a^{8\frac{1}{7}}\)

\(x^9⋅\sqrt[5]{x^2}=x^9⋅x^{\frac{2}{5}}=x^{9+\frac{2}{5}}=x^{9\frac{2}{5}}\)

\({x^4 \over \sqrt[9]{x^5}}={x^4 \over x^{\frac{5}{9}}}=x^{4-\frac{5}{9}}=x^{3\frac{4}{9}}\)

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

\({\sqrt[5]{x^4} \over \sqrt[5]{x^3}}={x^{\frac{4}{5}} \over x^{\frac{3}{5}}}=x^{\frac{4}{5}-\frac{3}{5}}=x^{\frac{1}{5}}\)

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

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

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

\({4q^2 \over 5p^6}\)

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

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

\(7p^{3\frac{3}{7}}=7⋅p^3⋅p^{\frac{3}{7}}=7p^3⋅\sqrt[7]{p^3}\)

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