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

\({x^8 \over x^{-9}}=x^{8--9}=x^{17}\)

\(a^3⋅a^{-9}=a^{3+-9}=a^{-6}\)

\((a^5)^{-9}=a^{5⋅-9}=a^{-45}\)

\(p^2⋅{1 \over p^7}=p^2⋅p^{-7}=p^{2+-7}=p^{-5}\)

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

\({a^8 \over a^0}=a^{8-0}=a^8\)

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

\({2x^2 \over 9x^4}={2 \over 9}⋅{x^2 \over x^4}={2 \over 9}⋅x^{2-4}={2 \over 9}x^{-2}\)

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

\({6a^4b \over 5ab^6}={6 \over 5}⋅{a^4 \over a^1}⋅{b^1 \over b^6}={6 \over 5}⋅a^{4-1}⋅a^{1-6}=1\frac{1}{5}a^3b^{-5}\)

\(p^2⋅\sqrt[5]{p}=p^2⋅p^{\frac{1}{5}}=p^{2+\frac{1}{5}}=p^{2\frac{1}{5}}\)

\(x^6⋅\sqrt[9]{x^4}=x^6⋅x^{\frac{4}{9}}=x^{6+\frac{4}{9}}=x^{6\frac{4}{9}}\)

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

\({1 \over a^9}⋅\sqrt[7]{a^3}=a^{-9}⋅a^{\frac{3}{7}}=a^{-9+\frac{3}{7}}=a^{-8\frac{4}{7}}\)

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

\(\sqrt[8]{{1 \over a^5}}=\sqrt[8]{a^{-5}}=a^{-\frac{5}{8}}\)

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

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

\({2b^9 \over 5a^3}\)

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

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

\(7x^{4\frac{3}{5}}=7⋅x^4⋅x^{\frac{3}{5}}=7x^4⋅\sqrt[5]{x^3}\)

\(\frac{4}{5}p^{-\frac{7}{9}}q^{\frac{8}{9}}=\frac{4}{5}⋅{1 \over p^{\frac{7}{9}}}⋅q^{\frac{8}{9}}={4⋅\sqrt[9]{q^8} \over 5⋅\sqrt[9]{p^7}}\)