Negatieve en gebroken exponenten

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

\({3a^5 \over 8a^8}={3 \over 8}⋅{a^5 \over a^8}={3 \over 8}⋅a^{5-8}={3 \over 8}a^{-3}\)

\({x^3 \over x^{-6}}=x^{3--6}=x^9\)

\({({1 \over p^8}) \over p^2}={p^{-8} \over p^2}=p^{-8-2}=p^{-10}\)

\({a^5 \over ({1 \over a^7})}={a^5 \over a^{-7}}=a^{5--7}=a^{12}\)

\({5x^4y^2 \over 3xy^7}={5 \over 3}⋅{x^4 \over x^1}⋅{y^2 \over y^7}={5 \over 3}⋅x^{4-1}⋅x^{2-7}=1\frac{2}{3}x^3y^{-5}\)

\({x^0 \over x^8}=x^{0-8}=x^{-8}\)

\((a^6)^{-3}=a^{6⋅-3}=a^{-18}\)

\(p^2⋅p^{-3}=p^{2+-3}=p^{-1}\)

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

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

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

\({p^9 \over \sqrt[8]{p^7}}={p^9 \over p^{\frac{7}{8}}}=p^{9-\frac{7}{8}}=p^{8\frac{1}{8}}\)

\({1 \over x^4}⋅\sqrt[9]{x^7}=x^{-4}⋅x^{\frac{7}{9}}=x^{-4+\frac{7}{9}}=x^{-3\frac{2}{9}}\)

\({\sqrt[8]{a^7} \over \sqrt[7]{a^3}}={a^{\frac{7}{8}} \over a^{\frac{3}{7}}}=a^{\frac{7}{8}-\frac{3}{7}}=a^{\frac{25}{56}}\)

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

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

\({p^8 \over p^2⋅\sqrt[9]{p^2}}={p^8 \over p^2⋅p^{\frac{2}{9}}}={p^8 \over p^{2\frac{2}{9}}}=p^{8-2\frac{2}{9}}=p^{5\frac{7}{9}}\)

\((4a)^{-3}=4^{-3}⋅a^{-3}={1 \over 4^3}⋅{1 \over a^3}={1 \over 64a^3}\)

\(({1 \over 3}a)^{-2}=(3^{-1}⋅a)^{-2}=(3^{-1})^{-2}⋅a^{-2}=3^2⋅a^{-2}={9 \over a^2}\)

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

\({2y^7 \over 5x^6}\)

\(6a^{7\frac{8}{9}}=6⋅a^7⋅a^{\frac{8}{9}}=6a^7⋅\sqrt[9]{a^8}\)

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