Negatieve en gebroken exponenten

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

\({4x \over 9x^3}={4 \over 9}⋅{x \over x^3}={4 \over 9}⋅x^{1-3}={4 \over 9}x^{-2}\)

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

\({({1 \over a^8}) \over a^7}={a^{-8} \over a^7}=a^{-8-7}=a^{-15}\)

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

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

\({a^0 \over a^8}=a^{0-8}=a^{-8}\)

\((p^3)^{-9}=p^{3⋅-9}=p^{-27}\)

\(x^5⋅x^{-8}=x^{5+-8}=x^{-3}\)

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

\(x^5⋅\sqrt[3]{x}=x^5⋅x^{\frac{1}{3}}=x^{5+\frac{1}{3}}=x^{5\frac{1}{3}}\)

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

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

\({1 \over a^4}⋅\sqrt[4]{a^3}=a^{-4}⋅a^{\frac{3}{4}}=a^{-4+\frac{3}{4}}=a^{-3\frac{1}{4}}\)

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

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

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

\({p^7 \over p^2⋅\sqrt[5]{p^3}}={p^7 \over p^2⋅p^{\frac{3}{5}}}={p^7 \over p^{2\frac{3}{5}}}=p^{7-2\frac{3}{5}}=p^{4\frac{2}{5}}\)

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

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

\({3 \over a^7}\)

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

\(5a^{7\frac{8}{9}}=5⋅a^7⋅a^{\frac{8}{9}}=5a^7⋅\sqrt[9]{a^8}\)

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