Negatieve en gebroken exponenten

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

\({7a^2 \over 9a^3}={7 \over 9}⋅{a^2 \over a^3}={7 \over 9}⋅a^{2-3}={7 \over 9}a^{-1}\)

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

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

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

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

\({x^0 \over x^9}=x^{0-9}=x^{-9}\)

\((p^4)^{-5}=p^{4⋅-5}=p^{-20}\)

\(a^5⋅a^{-9}=a^{5+-9}=a^{-4}\)

\(x^3⋅{1 \over x^5}=x^3⋅x^{-5}=x^{3+-5}=x^{-2}\)

\(x^5⋅\sqrt{x}=x^5⋅x^{\frac{1}{2}}=x^{5+\frac{1}{2}}=x^{5\frac{1}{2}}\)

\(a^6⋅\sqrt[9]{a^5}=a^6⋅a^{\frac{5}{9}}=a^{6+\frac{5}{9}}=a^{6\frac{5}{9}}\)

\({p^2 \over \sqrt[6]{p^5}}={p^2 \over p^{\frac{5}{6}}}=p^{2-\frac{5}{6}}=p^{1\frac{1}{6}}\)

\({1 \over a^9}⋅\sqrt[5]{a^3}=a^{-9}⋅a^{\frac{3}{5}}=a^{-9+\frac{3}{5}}=a^{-8\frac{2}{5}}\)

\({\sqrt[7]{x^5} \over \sqrt[9]{x^2}}={x^{\frac{5}{7}} \over x^{\frac{2}{9}}}=x^{\frac{5}{7}-\frac{2}{9}}=x^{\frac{31}{63}}\)

\(\sqrt[9]{{1 \over a^2}}=\sqrt[9]{a^{-2}}=a^{-\frac{2}{9}}\)

\(\sqrt{x^4}=x^{\frac{4}{2}}=x^2\)

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

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

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

\({2 \over x^4}\)

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

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

\(\frac{6}{7}a^{-\frac{4}{9}}b^{\frac{7}{9}}=\frac{6}{7}⋅{1 \over a^{\frac{4}{9}}}⋅b^{\frac{7}{9}}={6⋅\sqrt[9]{b^7} \over 7⋅\sqrt[9]{a^4}}\)