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

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

\(p^2⋅p^{-9}=p^{2+-9}=p^{-7}\)

\((a^3)^{-7}=a^{3⋅-7}=a^{-21}\)

\(a^8⋅{1 \over a^9}=a^8⋅a^{-9}=a^{8+-9}=a^{-1}\)

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

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

\({7 \over p^5}\)

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

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

\({9a^4b^3 \over 7a^2b^4}={9 \over 7}⋅{a^4 \over a^2}⋅{b^3 \over b^4}={9 \over 7}⋅a^{4-2}⋅a^{3-4}=1\frac{2}{7}a^2b^{-1}\)

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

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

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

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

\({\sqrt[9]{x^8} \over \sqrt[8]{x^3}}={x^{\frac{8}{9}} \over x^{\frac{3}{8}}}=x^{\frac{8}{9}-\frac{3}{8}}=x^{\frac{37}{72}}\)

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

\(\sqrt[5]{p^{15}}=p^{\frac{15}{5}}=p^3\)

\({x^4 \over x^3⋅\sqrt[5]{x^3}}={x^4 \over x^3⋅x^{\frac{3}{5}}}={x^4 \over x^{3\frac{3}{5}}}=x^{4-3\frac{3}{5}}=x^{\frac{2}{5}}\)

\({2b^5 \over 9a^8}\)

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

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

\(8a^{6\frac{2}{7}}=8⋅a^6⋅a^{\frac{2}{7}}=8a^6⋅\sqrt[7]{a^2}\)

\(\frac{1}{8}p^{-\frac{2}{5}}q^{\frac{3}{5}}=\frac{1}{8}⋅{1 \over p^{\frac{2}{5}}}⋅q^{\frac{3}{5}}={1⋅\sqrt[5]{q^3} \over 8⋅\sqrt[5]{p^2}}\)