Negatieve en gebroken exponenten

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

\({4a^3 \over 5a^8}={4 \over 5}⋅{a^3 \over a^8}={4 \over 5}⋅a^{3-8}={4 \over 5}a^{-5}\)

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

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

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

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

\({p^0 \over p^5}=p^{0-5}=p^{-5}\)

\((a^7)^{-5}=a^{7⋅-5}=a^{-35}\)

\(a^6⋅a^{-8}=a^{6+-8}=a^{-2}\)

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

\(p^3⋅\sqrt[7]{p}=p^3⋅p^{\frac{1}{7}}=p^{3+\frac{1}{7}}=p^{3\frac{1}{7}}\)

\(x^8⋅\sqrt[9]{x^4}=x^8⋅x^{\frac{4}{9}}=x^{8+\frac{4}{9}}=x^{8\frac{4}{9}}\)

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

\({1 \over a^2}⋅\sqrt[5]{a^2}=a^{-2}⋅a^{\frac{2}{5}}=a^{-2+\frac{2}{5}}=a^{-1\frac{3}{5}}\)

\({\sqrt[4]{x^3} \over \sqrt[8]{x^5}}={x^{\frac{3}{4}} \over x^{\frac{5}{8}}}=x^{\frac{3}{4}-\frac{5}{8}}=x^{\frac{1}{8}}\)

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

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

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

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

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

\({7 \over x^5}\)

\({2y^9 \over 3x^4}\)

\(7a^{2\frac{3}{5}}=7⋅a^2⋅a^{\frac{3}{5}}=7a^2⋅\sqrt[5]{a^3}\)

\(\frac{7}{9}a^{-\frac{7}{8}}b^{\frac{4}{5}}=\frac{7}{9}⋅{1 \over a^{\frac{7}{8}}}⋅b^{\frac{4}{5}}={7⋅\sqrt[5]{b^4} \over 9⋅\sqrt[8]{a^7}}\)