Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{1}}{x^{\frac{5}{6}}}\\= x^{ 1 - \frac{5}{6} }= x^{\frac{1}{6}}\\=\sqrt[6]{ x }\\---------------\)
2. \(\dfrac{a^{1}}{a^{-1}}\\= a^{ 1 - (-1) }= a^{2}\\\\---------------\)
3. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{3}{2}}}\\= a^{ \frac{-1}{2} - \frac{3}{2} }= a^{-2}\\=\frac{1}{a^{2}}\\---------------\)
4. \(\dfrac{q^{-1}}{q^{\frac{-1}{2}}}\\= q^{ -1 - (\frac{-1}{2}) }= q^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ q } }=\frac{1}{ \sqrt{ q } }. \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q|}\\---------------\)
5. \(\dfrac{y^{\frac{3}{5}}}{y^{\frac{-5}{3}}}\\= y^{ \frac{3}{5} - (\frac{-5}{3}) }= y^{\frac{34}{15}}\\=\sqrt[15]{ y^{34} }=y^{2}.\sqrt[15]{ y^{4} }\\---------------\)
6. \(\dfrac{y^{\frac{2}{5}}}{y^{\frac{1}{2}}}\\= y^{ \frac{2}{5} - \frac{1}{2} }= y^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ y }}=\frac{1}{\sqrt[10]{ y }}. \color{purple}{\frac{\sqrt[10]{ y^{9} }}{\sqrt[10]{ y^{9} }}} \\=\frac{\sqrt[10]{ y^{9} }}{|y|}\\---------------\)
7. \(\dfrac{a^{\frac{-5}{4}}}{a^{\frac{-4}{5}}}\\= a^{ \frac{-5}{4} - (\frac{-4}{5}) }= a^{\frac{-9}{20}}\\=\frac{1}{\sqrt[20]{ a^{9} }}=\frac{1}{\sqrt[20]{ a^{9} }}. \color{purple}{\frac{\sqrt[20]{ a^{11} }}{\sqrt[20]{ a^{11} }}} \\=\frac{\sqrt[20]{ a^{11} }}{|a|}\\---------------\)
8. \(\dfrac{q^{\frac{-2}{5}}}{q^{\frac{-1}{4}}}\\= q^{ \frac{-2}{5} - (\frac{-1}{4}) }= q^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ q^{3} }}=\frac{1}{\sqrt[20]{ q^{3} }}. \color{purple}{\frac{\sqrt[20]{ q^{17} }}{\sqrt[20]{ q^{17} }}} \\=\frac{\sqrt[20]{ q^{17} }}{|q|}\\---------------\)
9. \(\dfrac{a^{2}}{a^{\frac{2}{3}}}\\= a^{ 2 - \frac{2}{3} }= a^{\frac{4}{3}}\\=\sqrt[3]{ a^{4} }=a.\sqrt[3]{ a }\\---------------\)
10. \(\dfrac{y^{\frac{3}{2}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{3}{2} - (\frac{-1}{2}) }= y^{2}\\\\---------------\)
11. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{-1}{5}}}\\= x^{ \frac{1}{3} - (\frac{-1}{5}) }= x^{\frac{8}{15}}\\=\sqrt[15]{ x^{8} }\\---------------\)
12. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{1}{4}}}\\= x^{ \frac{1}{2} - \frac{1}{4} }= x^{\frac{1}{4}}\\=\sqrt[4]{ x }\\---------------\)