Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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