Negatieve en gebroken exponenten

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

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

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

\({({1 \over x^5}) \over x^4}={x^{-5} \over x^4}=x^{-5-4}=x^{-9}\)

\({a^7 \over ({1 \over a^9})}={a^7 \over a^{-9}}=a^{7--9}=a^{16}\)

\({9a^7b \over 7a^4b^6}={9 \over 7}⋅{a^7 \over a^4}⋅{b^1 \over b^6}={9 \over 7}⋅a^{7-4}⋅a^{1-6}=1\frac{2}{7}a^3b^{-5}\)

\({a^0 \over a^2}=a^{0-2}=a^{-2}\)

\((p^4)^{-6}=p^{4⋅-6}=p^{-24}\)

\(x^3⋅x^{-4}=x^{3+-4}=x^{-1}\)

\(x^6⋅{1 \over x^8}=x^6⋅x^{-8}=x^{6+-8}=x^{-2}\)

\(p^8⋅\sqrt{p}=p^8⋅p^{\frac{1}{2}}=p^{8+\frac{1}{2}}=p^{8\frac{1}{2}}\)

\(a^3⋅\sqrt[9]{a^8}=a^3⋅a^{\frac{8}{9}}=a^{3+\frac{8}{9}}=a^{3\frac{8}{9}}\)

\({x^7 \over \sqrt[4]{x^3}}={x^7 \over x^{\frac{3}{4}}}=x^{7-\frac{3}{4}}=x^{6\frac{1}{4}}\)

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

\({\sqrt[7]{x^3} \over \sqrt[9]{x^2}}={x^{\frac{3}{7}} \over x^{\frac{2}{9}}}=x^{\frac{3}{7}-\frac{2}{9}}=x^{\frac{13}{63}}\)

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

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

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

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

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

\({3 \over a^6}\)

\({2y^8 \over 7x^3}\)

\(7a^{8\frac{2}{9}}=7⋅a^8⋅a^{\frac{2}{9}}=7a^8⋅\sqrt[9]{a^2}\)

\(\frac{1}{9}x^{-\frac{5}{6}}y^{\frac{1}{8}}=\frac{1}{9}⋅{1 \over x^{\frac{5}{6}}}⋅y^{\frac{1}{8}}={1⋅\sqrt[8]{y} \over 9⋅\sqrt[6]{x^5}}\)