Negatieve en gebroken exponenten

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

\({8p^5 \over 9p^{10}}={8 \over 9}⋅{p^5 \over p^{10}}={8 \over 9}⋅p^{5-10}={8 \over 9}p^{-5}\)

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

\({({1 \over x^6}) \over x^4}={x^{-6} \over x^4}=x^{-6-4}=x^{-10}\)

\({x^6 \over ({1 \over x^9})}={x^6 \over x^{-9}}=x^{6--9}=x^{15}\)

\({7a^{10}b^4 \over 4a^5b^9}={7 \over 4}⋅{a^{10} \over a^5}⋅{b^4 \over b^9}={7 \over 4}⋅a^{10-5}⋅a^{4-9}=1\frac{3}{4}a^5b^{-5}\)

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

\((a^4)^{-8}=a^{4⋅-8}=a^{-32}\)

\(x^2⋅x^{-5}=x^{2+-5}=x^{-3}\)

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

\(x^3⋅\sqrt[9]{x}=x^3⋅x^{\frac{1}{9}}=x^{3+\frac{1}{9}}=x^{3\frac{1}{9}}\)

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

\({x^8 \over \sqrt[3]{x^2}}={x^8 \over x^{\frac{2}{3}}}=x^{8-\frac{2}{3}}=x^{7\frac{1}{3}}\)

\({1 \over p^8}⋅\sqrt[7]{p^5}=p^{-8}⋅p^{\frac{5}{7}}=p^{-8+\frac{5}{7}}=p^{-7\frac{2}{7}}\)

\({\sqrt[6]{a^5} \over \sqrt[8]{a^5}}={a^{\frac{5}{6}} \over a^{\frac{5}{8}}}=a^{\frac{5}{6}-\frac{5}{8}}=a^{\frac{5}{24}}\)

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

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

\({a^5 \over a^7⋅\sqrt[7]{a^6}}={a^5 \over a^7⋅a^{\frac{6}{7}}}={a^5 \over a^{7\frac{6}{7}}}=a^{5-7\frac{6}{7}}=a^{-2\frac{6}{7}}\)

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

\(({1 \over 2}x)^{-5}=(2^{-1}⋅x)^{-5}=(2^{-1})^{-5}⋅x^{-5}=2^5⋅x^{-5}={32 \over x^5}\)

\({7 \over a^9}\)

\({5b^2 \over 9a^5}\)

\(4x^{6\frac{3}{4}}=4⋅x^6⋅x^{\frac{3}{4}}=4x^6⋅\sqrt[4]{x^3}\)

\(\frac{5}{9}x^{-\frac{4}{5}}y^{\frac{5}{7}}=\frac{5}{9}⋅{1 \over x^{\frac{4}{5}}}⋅y^{\frac{5}{7}}={5⋅\sqrt[7]{y^5} \over 9⋅\sqrt[5]{x^4}}\)