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

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

\(x^2⋅x^{-6}=x^{2+-6}=x^{-4}\)

\((x^6)^{-5}=x^{6⋅-5}=x^{-30}\)

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

\({({1 \over x^9}) \over x^3}={x^{-9} \over x^3}=x^{-9-3}=x^{-12}\)

\({a^0 \over a^4}=a^{0-4}=a^{-4}\)

\({4 \over x^5}\)

\({3x^2 \over 4x^5}={3 \over 4}⋅{x^2 \over x^5}={3 \over 4}⋅x^{2-5}={3 \over 4}x^{-3}\)

\({a^3 \over ({1 \over a^6})}={a^3 \over a^{-6}}=a^{3--6}=a^9\)

\({7a^4b^2 \over 2ab^4}={7 \over 2}⋅{a^4 \over a^1}⋅{b^2 \over b^4}={7 \over 2}⋅a^{4-1}⋅a^{2-4}=3\frac{1}{2}a^3b^{-2}\)

\(x^3⋅\sqrt[7]{x}=x^3⋅x^{\frac{1}{7}}=x^{3+\frac{1}{7}}=x^{3\frac{1}{7}}\)

\(p^8⋅\sqrt[9]{p^5}=p^8⋅p^{\frac{5}{9}}=p^{8+\frac{5}{9}}=p^{8\frac{5}{9}}\)

\({a^2 \over \sqrt[9]{a^2}}={a^2 \over a^{\frac{2}{9}}}=a^{2-\frac{2}{9}}=a^{1\frac{7}{9}}\)

\({1 \over x^8}⋅\sqrt[7]{x^3}=x^{-8}⋅x^{\frac{3}{7}}=x^{-8+\frac{3}{7}}=x^{-7\frac{4}{7}}\)

\({\sqrt[3]{a^2} \over \sqrt[7]{a^4}}={a^{\frac{2}{3}} \over a^{\frac{4}{7}}}=a^{\frac{2}{3}-\frac{4}{7}}=a^{\frac{2}{21}}\)

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

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

\({p^2 \over p^9⋅\sqrt[9]{p^8}}={p^2 \over p^9⋅p^{\frac{8}{9}}}={p^2 \over p^{9\frac{8}{9}}}=p^{2-9\frac{8}{9}}=p^{-7\frac{8}{9}}\)

\({5y^5 \over 8x^4}\)

\((3a)^{-4}=3^{-4}⋅a^{-4}={1 \over 3^4}⋅{1 \over a^4}={1 \over 81a^4}\)

\(({1 \over 4}p)^{-3}=(4^{-1}⋅p)^{-3}=(4^{-1})^{-3}⋅p^{-3}=4^3⋅p^{-3}={64 \over p^3}\)

\(9x^{8\frac{3}{7}}=9⋅x^8⋅x^{\frac{3}{7}}=9x^8⋅\sqrt[7]{x^3}\)

\(\frac{1}{7}x^{-\frac{4}{9}}y^{\frac{2}{5}}=\frac{1}{7}⋅{1 \over x^{\frac{4}{9}}}⋅y^{\frac{2}{5}}={1⋅\sqrt[5]{y^2} \over 7⋅\sqrt[9]{x^4}}\)