Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-1}{2}}}{x^{-1}}\\= x^{ \frac{-1}{2} - (-1) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
2. \(\dfrac{y^{1}}{y^{\frac{2}{5}}}\\= y^{ 1 - \frac{2}{5} }= y^{\frac{3}{5}}\\=\sqrt[5]{ y^{3} }\\---------------\)
3. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-1}{6}}}\\= a^{ \frac{-1}{2} - (\frac{-1}{6}) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
4. \(\dfrac{y^{-2}}{y^{-2}}\\= y^{ -2 - (-2) }= y^{0}\\=1\\---------------\)
5. \(\dfrac{a^{\frac{2}{3}}}{a^{1}}\\= a^{ \frac{2}{3} - 1 }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
6. \(\dfrac{q^{\frac{3}{4}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{3}{4} - (\frac{-1}{3}) }= q^{\frac{13}{12}}\\=\sqrt[12]{ q^{13} }=|q|.\sqrt[12]{ q }\\---------------\)
7. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{-3}{2}}}\\= x^{ \frac{3}{4} - (\frac{-3}{2}) }= x^{\frac{9}{4}}\\=\sqrt[4]{ x^{9} }=|x^{2}|.\sqrt[4]{ x }\\---------------\)
8. \(\dfrac{q^{\frac{-3}{5}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{-3}{5} - (\frac{-1}{2}) }= q^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ q }}=\frac{1}{\sqrt[10]{ q }}. \color{purple}{\frac{\sqrt[10]{ q^{9} }}{\sqrt[10]{ q^{9} }}} \\=\frac{\sqrt[10]{ q^{9} }}{|q|}\\---------------\)
9. \(\dfrac{a^{\frac{5}{6}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{5}{6} - (\frac{-2}{3}) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
10. \(\dfrac{x^{\frac{4}{3}}}{x^{\frac{-5}{6}}}\\= x^{ \frac{4}{3} - (\frac{-5}{6}) }= x^{\frac{13}{6}}\\=\sqrt[6]{ x^{13} }=|x^{2}|.\sqrt[6]{ x }\\---------------\)
11. \(\dfrac{a^{\frac{1}{4}}}{a^{\frac{-1}{4}}}\\= a^{ \frac{1}{4} - (\frac{-1}{4}) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
12. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{-4}{5}}}\\= x^{ \frac{-1}{2} - (\frac{-4}{5}) }= x^{\frac{3}{10}}\\=\sqrt[10]{ x^{3} }\\---------------\)