Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{1}{6}}}\\= q^{ \frac{2}{3} - \frac{1}{6} }= q^{\frac{1}{2}}\\= \sqrt{ q } \\---------------\)
2. \(\dfrac{q^{\frac{-4}{3}}}{q^{\frac{-1}{5}}}\\= q^{ \frac{-4}{3} - (\frac{-1}{5}) }= q^{\frac{-17}{15}}\\=\frac{1}{\sqrt[15]{ q^{17} }}\\=\frac{1}{q.\sqrt[15]{ q^{2} }}=\frac{1}{q.\sqrt[15]{ q^{2} }} \color{purple}{\frac{\sqrt[15]{ q^{13} }}{\sqrt[15]{ q^{13} }}} \\=\frac{\sqrt[15]{ q^{13} }}{q^{2}}\\---------------\)
3. \(\dfrac{a^{2}}{a^{\frac{-2}{3}}}\\= a^{ 2 - (\frac{-2}{3}) }= a^{\frac{8}{3}}\\=\sqrt[3]{ a^{8} }=a^{2}.\sqrt[3]{ a^{2} }\\---------------\)
4. \(\dfrac{a^{\frac{-4}{5}}}{a^{\frac{-3}{2}}}\\= a^{ \frac{-4}{5} - (\frac{-3}{2}) }= a^{\frac{7}{10}}\\=\sqrt[10]{ a^{7} }\\---------------\)
5. \(\dfrac{y^{\frac{3}{5}}}{y^{\frac{1}{4}}}\\= y^{ \frac{3}{5} - \frac{1}{4} }= y^{\frac{7}{20}}\\=\sqrt[20]{ y^{7} }\\---------------\)
6. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{4}{5}}}\\= x^{ \frac{1}{2} - \frac{4}{5} }= x^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ x^{3} }}=\frac{1}{\sqrt[10]{ x^{3} }}. \color{purple}{\frac{\sqrt[10]{ x^{7} }}{\sqrt[10]{ x^{7} }}} \\=\frac{\sqrt[10]{ x^{7} }}{|x|}\\---------------\)
7. \(\dfrac{a^{\frac{-1}{4}}}{a^{-1}}\\= a^{ \frac{-1}{4} - (-1) }= a^{\frac{3}{4}}\\=\sqrt[4]{ a^{3} }\\---------------\)
8. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{-1}{5}}}\\= x^{ \frac{-1}{2} - (\frac{-1}{5}) }= x^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ x^{3} }}=\frac{1}{\sqrt[10]{ x^{3} }}. \color{purple}{\frac{\sqrt[10]{ x^{7} }}{\sqrt[10]{ x^{7} }}} \\=\frac{\sqrt[10]{ x^{7} }}{|x|}\\---------------\)
9. \(\dfrac{y^{\frac{-3}{5}}}{y^{\frac{-3}{2}}}\\= y^{ \frac{-3}{5} - (\frac{-3}{2}) }= y^{\frac{9}{10}}\\=\sqrt[10]{ y^{9} }\\---------------\)
10. \(\dfrac{a^{\frac{1}{4}}}{a^{\frac{2}{5}}}\\= a^{ \frac{1}{4} - \frac{2}{5} }= a^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ a^{3} }}=\frac{1}{\sqrt[20]{ a^{3} }}. \color{purple}{\frac{\sqrt[20]{ a^{17} }}{\sqrt[20]{ a^{17} }}} \\=\frac{\sqrt[20]{ a^{17} }}{|a|}\\---------------\)
11. \(\dfrac{a^{-1}}{a^{\frac{-1}{2}}}\\= a^{ -1 - (\frac{-1}{2}) }= a^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ a } }=\frac{1}{ \sqrt{ a } }. \color{purple}{\frac{ \sqrt{ a } }{ \sqrt{ a } }} \\=\frac{ \sqrt{ a } }{|a|}\\---------------\)
12. \(\dfrac{a^{\frac{-4}{3}}}{a^{-1}}\\= a^{ \frac{-4}{3} - (-1) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)