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

\({x^3 \over x^{-8}}=x^{3--8}=x^{11}\)

\(x^3⋅x^{-6}=x^{3+-6}=x^{-3}\)

\((a^6)^{-7}=a^{6⋅-7}=a^{-42}\)

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

\({({1 \over p^4}) \over p^2}={p^{-4} \over p^2}=p^{-4-2}=p^{-6}\)

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

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

\({7a^4 \over 8a^5}={7 \over 8}⋅{a^4 \over a^5}={7 \over 8}⋅a^{4-5}={7 \over 8}a^{-1}\)

\({p^3 \over ({1 \over p^7})}={p^3 \over p^{-7}}=p^{3--7}=p^{10}\)

\({6a^7b \over 5a^3b^3}={6 \over 5}⋅{a^7 \over a^3}⋅{b^1 \over b^3}={6 \over 5}⋅a^{7-3}⋅a^{1-3}=1\frac{1}{5}a^4b^{-2}\)

\(x^7⋅\sqrt[9]{x}=x^7⋅x^{\frac{1}{9}}=x^{7+\frac{1}{9}}=x^{7\frac{1}{9}}\)

\(a^8⋅\sqrt[7]{a^5}=a^8⋅a^{\frac{5}{7}}=a^{8+\frac{5}{7}}=a^{8\frac{5}{7}}\)

\({x^9 \over \sqrt[8]{x^7}}={x^9 \over x^{\frac{7}{8}}}=x^{9-\frac{7}{8}}=x^{8\frac{1}{8}}\)

\({1 \over p^6}⋅\sqrt[5]{p^3}=p^{-6}⋅p^{\frac{3}{5}}=p^{-6+\frac{3}{5}}=p^{-5\frac{2}{5}}\)

\({\sqrt[9]{x^5} \over \sqrt[7]{x^3}}={x^{\frac{5}{9}} \over x^{\frac{3}{7}}}=x^{\frac{5}{9}-\frac{3}{7}}=x^{\frac{8}{63}}\)

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

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

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

\({3b^9 \over 7a^4}\)

\((5x)^{-3}=5^{-3}⋅x^{-3}={1 \over 5^3}⋅{1 \over x^3}={1 \over 125x^3}\)

\(({1 \over 5}x)^{-3}=(5^{-1}⋅x)^{-3}=(5^{-1})^{-3}⋅x^{-3}=5^3⋅x^{-3}={125 \over x^3}\)

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

\(\frac{3}{4}a^{-\frac{7}{9}}b^{\frac{5}{9}}=\frac{3}{4}⋅{1 \over a^{\frac{7}{9}}}⋅b^{\frac{5}{9}}={3⋅\sqrt[9]{b^5} \over 4⋅\sqrt[9]{a^7}}\)