Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{5}{4}}}{a^{\frac{3}{2}}}\\= a^{ \frac{5}{4} - \frac{3}{2} }= a^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ a }}=\frac{1}{\sqrt[4]{ a }}. \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a|}\\---------------\)
2. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{2}{3}}}\\= x^{ \frac{1}{2} - \frac{2}{3} }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
3. \(\dfrac{q^{\frac{1}{3}}}{q^{-2}}\\= q^{ \frac{1}{3} - (-2) }= q^{\frac{7}{3}}\\=\sqrt[3]{ q^{7} }=q^{2}.\sqrt[3]{ q }\\---------------\)
4. \(\dfrac{x^{\frac{-5}{6}}}{x^{\frac{-3}{2}}}\\= x^{ \frac{-5}{6} - (\frac{-3}{2}) }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
5. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{-1}{5}}}\\= x^{ \frac{-1}{2} - (\frac{-1}{5}) }= x^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ x^{3} }}=\frac{1}{\sqrt[10]{ x^{3} }}. \color{purple}{\frac{\sqrt[10]{ x^{7} }}{\sqrt[10]{ x^{7} }}} \\=\frac{\sqrt[10]{ x^{7} }}{|x|}\\---------------\)
6. \(\dfrac{y^{\frac{-5}{6}}}{y^{-1}}\\= y^{ \frac{-5}{6} - (-1) }= y^{\frac{1}{6}}\\=\sqrt[6]{ y }\\---------------\)
7. \(\dfrac{q^{\frac{1}{2}}}{q^{1}}\\= q^{ \frac{1}{2} - 1 }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
8. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{-4}{5}}}\\= x^{ \frac{1}{3} - (\frac{-4}{5}) }= x^{\frac{17}{15}}\\=\sqrt[15]{ x^{17} }=x.\sqrt[15]{ x^{2} }\\---------------\)
9. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{3}{5}}}\\= x^{ \frac{-1}{3} - \frac{3}{5} }= x^{\frac{-14}{15}}\\=\frac{1}{\sqrt[15]{ x^{14} }}=\frac{1}{\sqrt[15]{ x^{14} }}. \color{purple}{\frac{\sqrt[15]{ x }}{\sqrt[15]{ x }}} \\=\frac{\sqrt[15]{ x }}{x}\\---------------\)
10. \(\dfrac{y^{1}}{y^{\frac{1}{2}}}\\= y^{ 1 - \frac{1}{2} }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
11. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-5}{4}}}\\= q^{ \frac{-1}{2} - (\frac{-5}{4}) }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)
12. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{-1}{3} - (\frac{-2}{3}) }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)