Negatieve en gebroken exponenten

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

\({2x \over 5x^3}={2 \over 5}⋅{x \over x^3}={2 \over 5}⋅x^{1-3}={2 \over 5}x^{-2}\)

\({a^8 \over a^{-9}}=a^{8--9}=a^{17}\)

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

\({x^4 \over ({1 \over x^8})}={x^4 \over x^{-8}}=x^{4--8}=x^{12}\)

\({8a^5b^3 \over 7a^4b^5}={8 \over 7}⋅{a^5 \over a^4}⋅{b^3 \over b^5}={8 \over 7}⋅a^{5-4}⋅a^{3-5}=1\frac{1}{7}ab^{-2}\)

\({p^7 \over p^0}=p^{7-0}=p^7\)

\((x^6)^{-5}=x^{6⋅-5}=x^{-30}\)

\(a^5⋅a^{-8}=a^{5+-8}=a^{-3}\)

\(x^3⋅{1 \over x^5}=x^3⋅x^{-5}=x^{3+-5}=x^{-2}\)

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

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

\({p^9 \over \sqrt[7]{p^3}}={p^9 \over p^{\frac{3}{7}}}=p^{9-\frac{3}{7}}=p^{8\frac{4}{7}}\)

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

\({\sqrt[7]{x^4} \over \sqrt[5]{x^2}}={x^{\frac{4}{7}} \over x^{\frac{2}{5}}}=x^{\frac{4}{7}-\frac{2}{5}}=x^{\frac{6}{35}}\)

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

\(\sqrt[4]{x^{20}}=x^{\frac{20}{4}}=x^5\)

\({a^2 \over a^8⋅\sqrt[7]{a^6}}={a^2 \over a^8⋅a^{\frac{6}{7}}}={a^2 \over a^{8\frac{6}{7}}}=a^{2-8\frac{6}{7}}=a^{-6\frac{6}{7}}\)

\((3p)^{-4}=3^{-4}⋅p^{-4}={1 \over 3^4}⋅{1 \over p^4}={1 \over 81p^4}\)

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

\({8 \over p^9}\)

\({4b^4 \over 5a^2}\)

\(4x^{9\frac{3}{4}}=4⋅x^9⋅x^{\frac{3}{4}}=4x^9⋅\sqrt[4]{x^3}\)

\(\frac{8}{9}a^{-\frac{3}{8}}b^{\frac{2}{7}}=\frac{8}{9}⋅{1 \over a^{\frac{3}{8}}}⋅b^{\frac{2}{7}}={8⋅\sqrt[7]{b^2} \over 9⋅\sqrt[8]{a^3}}\)