Negatieve en gebroken exponenten

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

\({8a^2 \over 9a^4}={8 \over 9}⋅{a^2 \over a^4}={8 \over 9}⋅a^{2-4}={8 \over 9}a^{-2}\)

\({x^9 \over x^{-4}}=x^{9--4}=x^{13}\)

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

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

\({4a^4b^3 \over 3a^2b^5}={4 \over 3}⋅{a^4 \over a^2}⋅{b^3 \over b^5}={4 \over 3}⋅a^{4-2}⋅a^{3-5}=1\frac{1}{3}a^2b^{-2}\)

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

\((x^4)^{-6}=x^{4⋅-6}=x^{-24}\)

\(a^4⋅a^{-5}=a^{4+-5}=a^{-1}\)

\(p^4⋅{1 \over p^5}=p^4⋅p^{-5}=p^{4+-5}=p^{-1}\)

\(p^3⋅\sqrt[6]{p}=p^3⋅p^{\frac{1}{6}}=p^{3+\frac{1}{6}}=p^{3\frac{1}{6}}\)

\(x^5⋅\sqrt[3]{x^2}=x^5⋅x^{\frac{2}{3}}=x^{5+\frac{2}{3}}=x^{5\frac{2}{3}}\)

\({x^5 \over \sqrt[8]{x^5}}={x^5 \over x^{\frac{5}{8}}}=x^{5-\frac{5}{8}}=x^{4\frac{3}{8}}\)

\({1 \over a^4}⋅\sqrt[8]{a^7}=a^{-4}⋅a^{\frac{7}{8}}=a^{-4+\frac{7}{8}}=a^{-3\frac{1}{8}}\)

\({\sqrt[7]{a^4} \over \sqrt[8]{a^3}}={a^{\frac{4}{7}} \over a^{\frac{3}{8}}}=a^{\frac{4}{7}-\frac{3}{8}}=a^{\frac{11}{56}}\)

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

\(\sqrt[5]{p^{25}}=p^{\frac{25}{5}}=p^5\)

\({a^4 \over a^9⋅\sqrt[7]{a^2}}={a^4 \over a^9⋅a^{\frac{2}{7}}}={a^4 \over a^{9\frac{2}{7}}}=a^{4-9\frac{2}{7}}=a^{-5\frac{2}{7}}\)

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

\(({1 \over 4}x)^{-5}=(4^{-1}⋅x)^{-5}=(4^{-1})^{-5}⋅x^{-5}=4^5⋅x^{-5}={1\,024 \over x^5}\)

\({6 \over p^8}\)

\({7y^9 \over 8x^8}\)

\(7x^{3\frac{5}{9}}=7⋅x^3⋅x^{\frac{5}{9}}=7x^3⋅\sqrt[9]{x^5}\)

\(\frac{3}{8}a^{-\frac{1}{5}}b^{\frac{3}{5}}=\frac{3}{8}⋅{1 \over a^{\frac{1}{5}}}⋅b^{\frac{3}{5}}={3⋅\sqrt[5]{b^3} \over 8⋅\sqrt[5]{a}}\)