Negatieve en gebroken exponenten

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

\({4p^4 \over 7p^8}={4 \over 7}⋅{p^4 \over p^8}={4 \over 7}⋅p^{4-8}={4 \over 7}p^{-4}\)

\({x^8 \over x^{-6}}=x^{8--6}=x^{14}\)

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

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

\({9x^4y \over 5x^3y^5}={9 \over 5}⋅{x^4 \over x^3}⋅{y^1 \over y^5}={9 \over 5}⋅x^{4-3}⋅x^{1-5}=1\frac{4}{5}xy^{-4}\)

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

\((p^2)^{-7}=p^{2⋅-7}=p^{-14}\)

\(a^3⋅a^{-7}=a^{3+-7}=a^{-4}\)

\(x^3⋅{1 \over x^6}=x^3⋅x^{-6}=x^{3+-6}=x^{-3}\)

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

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

\({a^2 \over \sqrt[5]{a^4}}={a^2 \over a^{\frac{4}{5}}}=a^{2-\frac{4}{5}}=a^{1\frac{1}{5}}\)

\({1 \over x^6}⋅\sqrt[9]{x^2}=x^{-6}⋅x^{\frac{2}{9}}=x^{-6+\frac{2}{9}}=x^{-5\frac{7}{9}}\)

\({\sqrt[4]{p^3} \over \sqrt[7]{p^5}}={p^{\frac{3}{4}} \over p^{\frac{5}{7}}}=p^{\frac{3}{4}-\frac{5}{7}}=p^{\frac{1}{28}}\)

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

\(\sqrt[4]{x^{16}}=x^{\frac{16}{4}}=x^4\)

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

\((5a)^{-3}=5^{-3}⋅a^{-3}={1 \over 5^3}⋅{1 \over a^3}={1 \over 125a^3}\)

\(({1 \over 2}p)^{-3}=(2^{-1}⋅p)^{-3}=(2^{-1})^{-3}⋅p^{-3}=2^3⋅p^{-3}={8 \over p^3}\)

\({4 \over p^9}\)

\({2y^6 \over 9x^8}\)

\(8x^{4\frac{3}{8}}=8⋅x^4⋅x^{\frac{3}{8}}=8x^4⋅\sqrt[8]{x^3}\)

\(\frac{4}{7}a^{-\frac{6}{7}}b^{\frac{5}{8}}=\frac{4}{7}⋅{1 \over a^{\frac{6}{7}}}⋅b^{\frac{5}{8}}={4⋅\sqrt[8]{b^5} \over 7⋅\sqrt[7]{a^6}}\)