Negatieve en gebroken exponenten

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

\({5x^2 \over 9x^5}={5 \over 9}⋅{x^2 \over x^5}={5 \over 9}⋅x^{2-5}={5 \over 9}x^{-3}\)

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

\({({1 \over a^7}) \over a^3}={a^{-7} \over a^3}=a^{-7-3}=a^{-10}\)

\({p^3 \over ({1 \over p^4})}={p^3 \over p^{-4}}=p^{3--4}=p^7\)

\({9a^7b^3 \over 7a^4b^6}={9 \over 7}⋅{a^7 \over a^4}⋅{b^3 \over b^6}={9 \over 7}⋅a^{7-4}⋅a^{3-6}=1\frac{2}{7}a^3b^{-3}\)

\({x^4 \over x^0}=x^{4-0}=x^4\)

\((x^3)^{-4}=x^{3⋅-4}=x^{-12}\)

\(a^6⋅a^{-8}=a^{6+-8}=a^{-2}\)

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

\(x^6⋅\sqrt[4]{x}=x^6⋅x^{\frac{1}{4}}=x^{6+\frac{1}{4}}=x^{6\frac{1}{4}}\)

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

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

\({1 \over a^8}⋅\sqrt[3]{a^2}=a^{-8}⋅a^{\frac{2}{3}}=a^{-8+\frac{2}{3}}=a^{-7\frac{1}{3}}\)

\({\sqrt[9]{x^5} \over \sqrt[8]{x^3}}={x^{\frac{5}{9}} \over x^{\frac{3}{8}}}=x^{\frac{5}{9}-\frac{3}{8}}=x^{\frac{13}{72}}\)

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

\(\sqrt{p^6}=p^{\frac{6}{2}}=p^3\)

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

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

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

\({9 \over a^5}\)

\({3b^3 \over 8a^9}\)

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

\(\frac{4}{7}x^{-\frac{7}{9}}y^{\frac{4}{5}}=\frac{4}{7}⋅{1 \over x^{\frac{7}{9}}}⋅y^{\frac{4}{5}}={4⋅\sqrt[5]{y^4} \over 7⋅\sqrt[9]{x^7}}\)