Negatieve en gebroken exponenten

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

\({5a^4 \over 9a^7}={5 \over 9}⋅{a^4 \over a^7}={5 \over 9}⋅a^{4-7}={5 \over 9}a^{-3}\)

\({a^2 \over a^{-9}}=a^{2--9}=a^{11}\)

\({({1 \over p^8}) \over p^7}={p^{-8} \over p^7}=p^{-8-7}=p^{-15}\)

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

\({7a^6b \over 6a^2b^5}={7 \over 6}⋅{a^6 \over a^2}⋅{b^1 \over b^5}={7 \over 6}⋅a^{6-2}⋅a^{1-5}=1\frac{1}{6}a^4b^{-4}\)

\({p^9 \over p^0}=p^{9-0}=p^9\)

\((x^5)^{-4}=x^{5⋅-4}=x^{-20}\)

\(x^2⋅x^{-8}=x^{2+-8}=x^{-6}\)

\(a^2⋅{1 \over a^8}=a^2⋅a^{-8}=a^{2+-8}=a^{-6}\)

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

\(x^6⋅\sqrt[8]{x^7}=x^6⋅x^{\frac{7}{8}}=x^{6+\frac{7}{8}}=x^{6\frac{7}{8}}\)

\({x^3 \over \sqrt[7]{x^6}}={x^3 \over x^{\frac{6}{7}}}=x^{3-\frac{6}{7}}=x^{2\frac{1}{7}}\)

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

\({\sqrt[5]{a^4} \over \sqrt[8]{a^5}}={a^{\frac{4}{5}} \over a^{\frac{5}{8}}}=a^{\frac{4}{5}-\frac{5}{8}}=a^{\frac{7}{40}}\)

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

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

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

\((5x)^{-2}=5^{-2}⋅x^{-2}={1 \over 5^2}⋅{1 \over x^2}={1 \over 25x^2}\)

\(({1 \over 3}a)^{-5}=(3^{-1}⋅a)^{-5}=(3^{-1})^{-5}⋅a^{-5}=3^5⋅a^{-5}={243 \over a^5}\)

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

\({8y^6 \over 9x^8}\)

\(2a^{7\frac{3}{7}}=2⋅a^7⋅a^{\frac{3}{7}}=2a^7⋅\sqrt[7]{a^3}\)

\(\frac{2}{5}a^{-\frac{2}{7}}b^{\frac{5}{7}}=\frac{2}{5}⋅{1 \over a^{\frac{2}{7}}}⋅b^{\frac{5}{7}}={2⋅\sqrt[7]{b^5} \over 5⋅\sqrt[7]{a^2}}\)