Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{1}}{x^{\frac{1}{4}}}\\= x^{ 1 - \frac{1}{4} }= x^{\frac{3}{4}}\\=\sqrt[4]{ x^{3} }\\---------------\)
2. \(\dfrac{x^{\frac{2}{5}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{2}{5} - (\frac{-1}{3}) }= x^{\frac{11}{15}}\\=\sqrt[15]{ x^{11} }\\---------------\)
3. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{-1}{2} - (\frac{-2}{3}) }= a^{\frac{1}{6}}\\=\sqrt[6]{ a }\\---------------\)
4. \(\dfrac{a^{\frac{1}{2}}}{a^{-1}}\\= a^{ \frac{1}{2} - (-1) }= a^{\frac{3}{2}}\\= \sqrt{ a^{3} } =|a|. \sqrt{ a } \\---------------\)
5. \(\dfrac{a^{\frac{1}{2}}}{a^{1}}\\= a^{ \frac{1}{2} - 1 }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
6. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{-1}{6}}}\\= q^{ \frac{1}{2} - (\frac{-1}{6}) }= q^{\frac{2}{3}}\\=\sqrt[3]{ q^{2} }\\---------------\)
7. \(\dfrac{y^{\frac{-3}{5}}}{y^{\frac{-1}{6}}}\\= y^{ \frac{-3}{5} - (\frac{-1}{6}) }= y^{\frac{-13}{30}}\\=\frac{1}{\sqrt[30]{ y^{13} }}=\frac{1}{\sqrt[30]{ y^{13} }}. \color{purple}{\frac{\sqrt[30]{ y^{17} }}{\sqrt[30]{ y^{17} }}} \\=\frac{\sqrt[30]{ y^{17} }}{|y|}\\---------------\)
8. \(\dfrac{q^{\frac{4}{3}}}{q^{-1}}\\= q^{ \frac{4}{3} - (-1) }= q^{\frac{7}{3}}\\=\sqrt[3]{ q^{7} }=q^{2}.\sqrt[3]{ q }\\---------------\)
9. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{1}{6}}}\\= q^{ \frac{1}{2} - \frac{1}{6} }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)
10. \(\dfrac{y^{\frac{5}{4}}}{y^{\frac{-5}{2}}}\\= y^{ \frac{5}{4} - (\frac{-5}{2}) }= y^{\frac{15}{4}}\\=\sqrt[4]{ y^{15} }=|y^{3}|.\sqrt[4]{ y^{3} }\\---------------\)
11. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{-1}{3} - (\frac{-1}{2}) }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
12. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{-3}{4}}}\\= q^{ \frac{2}{3} - (\frac{-3}{4}) }= q^{\frac{17}{12}}\\=\sqrt[12]{ q^{17} }=|q|.\sqrt[12]{ q^{5} }\\---------------\)