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

\({p^6 \over p^{-8}}=p^{6--8}=p^{14}\)

\(a^4⋅a^{-8}=a^{4+-8}=a^{-4}\)

\((a^9)^{-8}=a^{9⋅-8}=a^{-72}\)

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

\({({1 \over a^5}) \over a^4}={a^{-5} \over a^4}=a^{-5-4}=a^{-9}\)

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

\({8 \over p^5}\)

\({4x^2 \over 7x^7}={4 \over 7}⋅{x^2 \over x^7}={4 \over 7}⋅x^{2-7}={4 \over 7}x^{-5}\)

\({x^2 \over ({1 \over x^7})}={x^2 \over x^{-7}}=x^{2--7}=x^9\)

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

\(x^6⋅\sqrt[8]{x}=x^6⋅x^{\frac{1}{8}}=x^{6+\frac{1}{8}}=x^{6\frac{1}{8}}\)

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

\({a^7 \over \sqrt[3]{a^2}}={a^7 \over a^{\frac{2}{3}}}=a^{7-\frac{2}{3}}=a^{6\frac{1}{3}}\)

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

\({\sqrt[9]{a^7} \over \sqrt[7]{a^2}}={a^{\frac{7}{9}} \over a^{\frac{2}{7}}}=a^{\frac{7}{9}-\frac{2}{7}}=a^{\frac{31}{63}}\)

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

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

\({x^4 \over x^6⋅\sqrt[9]{x^4}}={x^4 \over x^6⋅x^{\frac{4}{9}}}={x^4 \over x^{6\frac{4}{9}}}=x^{4-6\frac{4}{9}}=x^{-2\frac{4}{9}}\)

\({3b^4 \over 5a^7}\)

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

\(({1 \over 2}p)^{-5}=(2^{-1}⋅p)^{-5}=(2^{-1})^{-5}⋅p^{-5}=2^5⋅p^{-5}={32 \over p^5}\)

\(2a^{3\frac{6}{7}}=2⋅a^3⋅a^{\frac{6}{7}}=2a^3⋅\sqrt[7]{a^6}\)

\(\frac{2}{9}p^{-\frac{1}{5}}q^{\frac{3}{7}}=\frac{2}{9}⋅{1 \over p^{\frac{1}{5}}}⋅q^{\frac{3}{7}}={2⋅\sqrt[7]{q^3} \over 9⋅\sqrt[5]{p}}\)