Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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