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

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

\(a^4⋅a^{-7}=a^{4+-7}=a^{-3}\)

\((a^6)^{-9}=a^{6⋅-9}=a^{-54}\)

\(x^6⋅{1 \over x^9}=x^6⋅x^{-9}=x^{6+-9}=x^{-3}\)

\({({1 \over p^8}) \over p^7}={p^{-8} \over p^7}=p^{-8-7}=p^{-15}\)

\({x^0 \over x^6}=x^{0-6}=x^{-6}\)

\({8 \over a^3}\)

\({2a^4 \over 7a^8}={2 \over 7}⋅{a^4 \over a^8}={2 \over 7}⋅a^{4-8}={2 \over 7}a^{-4}\)

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

\({8x^7y^2 \over 5x^2y^6}={8 \over 5}⋅{x^7 \over x^2}⋅{y^2 \over y^6}={8 \over 5}⋅x^{7-2}⋅x^{2-6}=1\frac{3}{5}x^5y^{-4}\)

\(a^7⋅\sqrt[5]{a}=a^7⋅a^{\frac{1}{5}}=a^{7+\frac{1}{5}}=a^{7\frac{1}{5}}\)

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

\({a^5 \over \sqrt[7]{a^6}}={a^5 \over a^{\frac{6}{7}}}=a^{5-\frac{6}{7}}=a^{4\frac{1}{7}}\)

\({1 \over p^7}⋅\sqrt[8]{p^7}=p^{-7}⋅p^{\frac{7}{8}}=p^{-7+\frac{7}{8}}=p^{-6\frac{1}{8}}\)

\({\sqrt[6]{a^5} \over \sqrt[7]{a^2}}={a^{\frac{5}{6}} \over a^{\frac{2}{7}}}=a^{\frac{5}{6}-\frac{2}{7}}=a^{\frac{23}{42}}\)

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

\(\sqrt[4]{a^{16}}=a^{\frac{16}{4}}=a^4\)

\({p^2 \over p^6⋅\sqrt[8]{p^3}}={p^2 \over p^6⋅p^{\frac{3}{8}}}={p^2 \over p^{6\frac{3}{8}}}=p^{2-6\frac{3}{8}}=p^{-4\frac{3}{8}}\)

\({3b^6 \over 7a^4}\)

\((5x)^{-4}=5^{-4}⋅x^{-4}={1 \over 5^4}⋅{1 \over x^4}={1 \over 625x^4}\)

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

\(6x^{7\frac{6}{7}}=6⋅x^7⋅x^{\frac{6}{7}}=6x^7⋅\sqrt[7]{x^6}\)

\(\frac{2}{9}p^{-\frac{1}{5}}q^{\frac{4}{5}}=\frac{2}{9}⋅{1 \over p^{\frac{1}{5}}}⋅q^{\frac{4}{5}}={2⋅\sqrt[5]{q^4} \over 9⋅\sqrt[5]{p}}\)