Negatieve en gebroken exponenten

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

\({6p^5 \over 7p^9}={6 \over 7}⋅{p^5 \over p^9}={6 \over 7}⋅p^{5-9}={6 \over 7}p^{-4}\)

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

\({({1 \over x^9}) \over x^3}={x^{-9} \over x^3}=x^{-9-3}=x^{-12}\)

\({a^3 \over ({1 \over a^7})}={a^3 \over a^{-7}}=a^{3--7}=a^{10}\)

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

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

\((x^4)^{-6}=x^{4⋅-6}=x^{-24}\)

\(x^4⋅x^{-6}=x^{4+-6}=x^{-2}\)

\(a^3⋅{1 \over a^9}=a^3⋅a^{-9}=a^{3+-9}=a^{-6}\)

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

\(a^2⋅\sqrt[9]{a^4}=a^2⋅a^{\frac{4}{9}}=a^{2+\frac{4}{9}}=a^{2\frac{4}{9}}\)

\({a^7 \over \sqrt[9]{a^2}}={a^7 \over a^{\frac{2}{9}}}=a^{7-\frac{2}{9}}=a^{6\frac{7}{9}}\)

\({1 \over p^5}⋅\sqrt[7]{p^5}=p^{-5}⋅p^{\frac{5}{7}}=p^{-5+\frac{5}{7}}=p^{-4\frac{2}{7}}\)

\({\sqrt[3]{x^2} \over \sqrt[7]{x^4}}={x^{\frac{2}{3}} \over x^{\frac{4}{7}}}=x^{\frac{2}{3}-\frac{4}{7}}=x^{\frac{2}{21}}\)

\(\sqrt[9]{{1 \over a^7}}=\sqrt[9]{a^{-7}}=a^{-\frac{7}{9}}\)

\(\sqrt[3]{p^{15}}=p^{\frac{15}{3}}=p^5\)

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

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

\(({1 \over 5}a)^{-4}=(5^{-1}⋅a)^{-4}=(5^{-1})^{-4}⋅a^{-4}=5^4⋅a^{-4}={625 \over a^4}\)

\({5 \over x^8}\)

\({3b^9 \over 7a^6}\)

\(4p^{6\frac{4}{9}}=4⋅p^6⋅p^{\frac{4}{9}}=4p^6⋅\sqrt[9]{p^4}\)

\(\frac{5}{6}x^{-\frac{1}{6}}y^{\frac{1}{3}}=\frac{5}{6}⋅{1 \over x^{\frac{1}{6}}}⋅y^{\frac{1}{3}}={5⋅\sqrt[3]{y} \over 6⋅\sqrt[6]{x}}\)