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

\({p^3 \over p^{-9}}=p^{3--9}=p^{12}\)

\(x^2⋅x^{-6}=x^{2+-6}=x^{-4}\)

\((a^5)^{-3}=a^{5⋅-3}=a^{-15}\)

\(a^6⋅{1 \over a^7}=a^6⋅a^{-7}=a^{6+-7}=a^{-1}\)

\({({1 \over x^5}) \over x^3}={x^{-5} \over x^3}=x^{-5-3}=x^{-8}\)

\({x^0 \over x^3}=x^{0-3}=x^{-3}\)

\({6 \over a^7}\)

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

\({x^5 \over ({1 \over x^6})}={x^5 \over x^{-6}}=x^{5--6}=x^{11}\)

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

\(p^7⋅\sqrt[4]{p}=p^7⋅p^{\frac{1}{4}}=p^{7+\frac{1}{4}}=p^{7\frac{1}{4}}\)

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

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

\({1 \over a^5}⋅\sqrt[9]{a^8}=a^{-5}⋅a^{\frac{8}{9}}=a^{-5+\frac{8}{9}}=a^{-4\frac{1}{9}}\)

\({\sqrt[9]{x^4} \over \sqrt[7]{x^3}}={x^{\frac{4}{9}} \over x^{\frac{3}{7}}}=x^{\frac{4}{9}-\frac{3}{7}}=x^{\frac{1}{63}}\)

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

\(\sqrt{a^4}=a^{\frac{4}{2}}=a^2\)

\({x^2 \over x^6⋅\sqrt[5]{x^2}}={x^2 \over x^6⋅x^{\frac{2}{5}}}={x^2 \over x^{6\frac{2}{5}}}=x^{2-6\frac{2}{5}}=x^{-4\frac{2}{5}}\)

\({3q^4 \over 7p^2}\)

\((2a)^{-4}=2^{-4}⋅a^{-4}={1 \over 2^4}⋅{1 \over a^4}={1 \over 16a^4}\)

\(({1 \over 3}x)^{-4}=(3^{-1}⋅x)^{-4}=(3^{-1})^{-4}⋅x^{-4}=3^4⋅x^{-4}={81 \over x^4}\)

\(7a^{5\frac{6}{7}}=7⋅a^5⋅a^{\frac{6}{7}}=7a^5⋅\sqrt[7]{a^6}\)

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