Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

1. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-5}{4}}}\)
2. \(\dfrac{x^{\frac{4}{5}}}{x^{\frac{-5}{6}}}\)
3. \(\dfrac{a^{\frac{-3}{5}}}{a^{\frac{4}{5}}}\)
4. \(\dfrac{q^{1}}{q^{\frac{-3}{2}}}\)
5. \(\dfrac{x^{\frac{3}{2}}}{x^{\frac{-5}{6}}}\)
6. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{3}{5}}}\)
7. \(\dfrac{y^{\frac{5}{3}}}{y^{-1}}\)
8. \(\dfrac{x^{1}}{x^{-2}}\)
9. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{2}{3}}}\)
10. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{4}{3}}}\)
11. \(\dfrac{y^{\frac{-5}{2}}}{y^{\frac{1}{2}}}\)
12. \(\dfrac{q^{1}}{q^{\frac{-1}{2}}}\)

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-5}{4}}}\\= a^{ \frac{-1}{2} - (\frac{-5}{4}) }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)
2. \(\dfrac{x^{\frac{4}{5}}}{x^{\frac{-5}{6}}}\\= x^{ \frac{4}{5} - (\frac{-5}{6}) }= x^{\frac{49}{30}}\\=\sqrt[30]{ x^{49} }=|x|.\sqrt[30]{ x^{19} }\\---------------\)
3. \(\dfrac{a^{\frac{-3}{5}}}{a^{\frac{4}{5}}}\\= a^{ \frac{-3}{5} - \frac{4}{5} }= a^{\frac{-7}{5}}\\=\frac{1}{\sqrt[5]{ a^{7} }}\\=\frac{1}{a.\sqrt[5]{ a^{2} }}=\frac{1}{a.\sqrt[5]{ a^{2} }} \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a^{2}}\\---------------\)
4. \(\dfrac{q^{1}}{q^{\frac{-3}{2}}}\\= q^{ 1 - (\frac{-3}{2}) }= q^{\frac{5}{2}}\\= \sqrt{ q^{5} } =|q^{2}|. \sqrt{ q } \\---------------\)
5. \(\dfrac{x^{\frac{3}{2}}}{x^{\frac{-5}{6}}}\\= x^{ \frac{3}{2} - (\frac{-5}{6}) }= x^{\frac{7}{3}}\\=\sqrt[3]{ x^{7} }=x^{2}.\sqrt[3]{ x }\\---------------\)
6. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{3}{5}}}\\= y^{ \frac{-1}{2} - \frac{3}{5} }= y^{\frac{-11}{10}}\\=\frac{1}{\sqrt[10]{ y^{11} }}\\=\frac{1}{|y|.\sqrt[10]{ y }}=\frac{1}{|y|.\sqrt[10]{ y }} \color{purple}{\frac{\sqrt[10]{ y^{9} }}{\sqrt[10]{ y^{9} }}} \\=\frac{\sqrt[10]{ y^{9} }}{|y^{2}|}\\---------------\)
7. \(\dfrac{y^{\frac{5}{3}}}{y^{-1}}\\= y^{ \frac{5}{3} - (-1) }= y^{\frac{8}{3}}\\=\sqrt[3]{ y^{8} }=y^{2}.\sqrt[3]{ y^{2} }\\---------------\)
8. \(\dfrac{x^{1}}{x^{-2}}\\= x^{ 1 - (-2) }= x^{3}\\\\---------------\)
9. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{2}{3}}}\\= x^{ \frac{1}{2} - \frac{2}{3} }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
10. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{4}{3}}}\\= a^{ \frac{-1}{2} - \frac{4}{3} }= a^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ a^{11} }}\\=\frac{1}{|a|.\sqrt[6]{ a^{5} }}=\frac{1}{|a|.\sqrt[6]{ a^{5} }} \color{purple}{\frac{\sqrt[6]{ a }}{\sqrt[6]{ a }}} \\=\frac{\sqrt[6]{ a }}{|a^{2}|}\\---------------\)
11. \(\dfrac{y^{\frac{-5}{2}}}{y^{\frac{1}{2}}}\\= y^{ \frac{-5}{2} - \frac{1}{2} }= y^{-3}\\=\frac{1}{y^{3}}\\---------------\)
12. \(\dfrac{q^{1}}{q^{\frac{-1}{2}}}\\= q^{ 1 - (\frac{-1}{2}) }= q^{\frac{3}{2}}\\= \sqrt{ q^{3} } =|q|. \sqrt{ q } \\---------------\)