Negatieve en gebroken exponenten

${1 \over a^4}=a^{-4}$

${3a^5 \over 7a^6}={3 \over 7}⋅{a^5 \over a^6}={3 \over 7}⋅a^{5-6}={3 \over 7}a^{-1}$

${x^2 \over x^{-7}}=x^{2--7}=x^9$

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

${x^2 \over ({1 \over x^7})}={x^2 \over x^{-7}}=x^{2--7}=x^9$

${9x^{10}y^3 \over 8x^5y^4}={9 \over 8}⋅{x^{10} \over x^5}⋅{y^3 \over y^4}={9 \over 8}⋅x^{10-5}⋅x^{3-4}=1\frac{1}{8}x^5y^{-1}$

${a^5 \over a^0}=a^{5-0}=a^5$

$(p^8)^{-9}=p^{8⋅-9}=p^{-72}$

$x^6⋅x^{-7}=x^{6+-7}=x^{-1}$

$a^2⋅{1 \over a^6}=a^2⋅a^{-6}=a^{2+-6}=a^{-4}$

$a^6⋅\sqrt[3]{a}=a^6⋅a^{\frac{1}{3}}=a^{6+\frac{1}{3}}=a^{6\frac{1}{3}}$

$a^5⋅\sqrt[4]{a^3}=a^5⋅a^{\frac{3}{4}}=a^{5+\frac{3}{4}}=a^{5\frac{3}{4}}$

${x^8 \over \sqrt[4]{x^3}}={x^8 \over x^{\frac{3}{4}}}=x^{8-\frac{3}{4}}=x^{7\frac{1}{4}}$

${1 \over x^7}⋅\sqrt[5]{x^3}=x^{-7}⋅x^{\frac{3}{5}}=x^{-7+\frac{3}{5}}=x^{-6\frac{2}{5}}$

${\sqrt[5]{p^4} \over \sqrt[3]{p^2}}={p^{\frac{4}{5}} \over p^{\frac{2}{3}}}=p^{\frac{4}{5}-\frac{2}{3}}=p^{\frac{2}{15}}$

$\sqrt[5]{{1 \over p^3}}=\sqrt[5]{p^{-3}}=p^{-\frac{3}{5}}$

$\sqrt[4]{x^{20}}=x^{\frac{20}{4}}=x^5$

${x^7 \over x^8⋅\sqrt[9]{x^8}}={x^7 \over x^8⋅x^{\frac{8}{9}}}={x^7 \over x^{8\frac{8}{9}}}=x^{7-8\frac{8}{9}}=x^{-1\frac{8}{9}}$

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

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

${3 \over p^7}$

${4b^6 \over 5a^2}$

$7x^{9\frac{4}{5}}=7⋅x^9⋅x^{\frac{4}{5}}=7x^9⋅\sqrt[5]{x^4}$

$\frac{3}{7}x^{-\frac{1}{6}}y^{\frac{1}{3}}=\frac{3}{7}⋅{1 \over x^{\frac{1}{6}}}⋅y^{\frac{1}{3}}={3⋅\sqrt[3]{y} \over 7⋅\sqrt[6]{x}}$