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

\({a^6 \over a^{-5}}=a^{6--5}=a^{11}\)

\(p^4⋅p^{-6}=p^{4+-6}=p^{-2}\)

\((a^5)^{-2}=a^{5⋅-2}=a^{-10}\)

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

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

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

\({4 \over x^6}\)

\({3x^2 \over 7x^6}={3 \over 7}⋅{x^2 \over x^6}={3 \over 7}⋅x^{2-6}={3 \over 7}x^{-4}\)

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

\({9x^7y \over 8x^2y^3}={9 \over 8}⋅{x^7 \over x^2}⋅{y^1 \over y^3}={9 \over 8}⋅x^{7-2}⋅x^{1-3}=1\frac{1}{8}x^5y^{-2}\)

\(a^8⋅\sqrt{a}=a^8⋅a^{\frac{1}{2}}=a^{8+\frac{1}{2}}=a^{8\frac{1}{2}}\)

\(p^6⋅\sqrt[9]{p^8}=p^6⋅p^{\frac{8}{9}}=p^{6+\frac{8}{9}}=p^{6\frac{8}{9}}\)

\({a^5 \over \sqrt[5]{a^2}}={a^5 \over a^{\frac{2}{5}}}=a^{5-\frac{2}{5}}=a^{4\frac{3}{5}}\)

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

\({\sqrt[3]{a^2} \over \sqrt[7]{a^4}}={a^{\frac{2}{3}} \over a^{\frac{4}{7}}}=a^{\frac{2}{3}-\frac{4}{7}}=a^{\frac{2}{21}}\)

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

\(\sqrt[4]{x^8}=x^{\frac{8}{4}}=x^2\)

\({a^3 \over a^2⋅\sqrt[8]{a^3}}={a^3 \over a^2⋅a^{\frac{3}{8}}}={a^3 \over a^{2\frac{3}{8}}}=a^{3-2\frac{3}{8}}=a^{\frac{5}{8}}\)

\({4q^7 \over 5p^3}\)

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

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

\(2p^{5\frac{7}{8}}=2⋅p^5⋅p^{\frac{7}{8}}=2p^5⋅\sqrt[8]{p^7}\)

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