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

\({5a^5 \over 7a^{10}}={5 \over 7}⋅{a^5 \over a^{10}}={5 \over 7}⋅a^{5-10}={5 \over 7}a^{-5}\)

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

\(p^2⋅p^{-9}=p^{2+-9}=p^{-7}\)

\((x^5)^{-3}=x^{5⋅-3}=x^{-15}\)

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

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

\({a^2 \over ({1 \over a^6})}={a^2 \over a^{-6}}=a^{2--6}=a^8\)

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

\({x^7 \over x^0}=x^{7-0}=x^7\)

\(a^8⋅\sqrt[5]{a}=a^8⋅a^{\frac{1}{5}}=a^{8+\frac{1}{5}}=a^{8\frac{1}{5}}\)

\(a^9⋅\sqrt[5]{a^4}=a^9⋅a^{\frac{4}{5}}=a^{9+\frac{4}{5}}=a^{9\frac{4}{5}}\)

\({x^4 \over \sqrt[7]{x^6}}={x^4 \over x^{\frac{6}{7}}}=x^{4-\frac{6}{7}}=x^{3\frac{1}{7}}\)

\({1 \over a^8}⋅\sqrt[6]{a^5}=a^{-8}⋅a^{\frac{5}{6}}=a^{-8+\frac{5}{6}}=a^{-7\frac{1}{6}}\)

\({\sqrt[9]{p^7} \over \sqrt[7]{p^4}}={p^{\frac{7}{9}} \over p^{\frac{4}{7}}}=p^{\frac{7}{9}-\frac{4}{7}}=p^{\frac{13}{63}}\)

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

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

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

\({8 \over x^2}\)

\({4q^2 \over 7p^6}\)

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

\(6a^{9\frac{3}{4}}=6⋅a^9⋅a^{\frac{3}{4}}=6a^9⋅\sqrt[4]{a^3}\)

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

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