Negatieve en gebroken exponenten

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

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

\({a^7 \over a^{-6}}=a^{7--6}=a^{13}\)

\({({1 \over a^9}) \over a^5}={a^{-9} \over a^5}=a^{-9-5}=a^{-14}\)

\({x^2 \over ({1 \over x^5})}={x^2 \over x^{-5}}=x^{2--5}=x^7\)

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

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

\((x^4)^{-8}=x^{4⋅-8}=x^{-32}\)

\(p^5⋅p^{-6}=p^{5+-6}=p^{-1}\)

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

\(x^6⋅\sqrt{x}=x^6⋅x^{\frac{1}{2}}=x^{6+\frac{1}{2}}=x^{6\frac{1}{2}}\)

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

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

\({1 \over p^9}⋅\sqrt[8]{p^3}=p^{-9}⋅p^{\frac{3}{8}}=p^{-9+\frac{3}{8}}=p^{-8\frac{5}{8}}\)

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

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

\(\sqrt[5]{p^{15}}=p^{\frac{15}{5}}=p^3\)

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

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

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

\({7 \over a^2}\)

\({3b^6 \over 7a^4}\)

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

\(\frac{7}{9}p^{-\frac{5}{6}}q^{\frac{7}{8}}=\frac{7}{9}⋅{1 \over p^{\frac{5}{6}}}⋅q^{\frac{7}{8}}={7⋅\sqrt[8]{q^7} \over 9⋅\sqrt[6]{p^5}}\)