Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{-1}{4}}}\\= q^{ \frac{2}{5} - (\frac{-1}{4}) }= q^{\frac{13}{20}}\\=\sqrt[20]{ q^{13} }\\---------------\)
2. \(\dfrac{q^{\frac{3}{2}}}{q^{\frac{-3}{2}}}\\= q^{ \frac{3}{2} - (\frac{-3}{2}) }= q^{3}\\\\---------------\)
3. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{2}{5}}}\\= y^{ \frac{1}{2} - \frac{2}{5} }= y^{\frac{1}{10}}\\=\sqrt[10]{ y }\\---------------\)
4. \(\dfrac{q^{2}}{q^{\frac{-2}{3}}}\\= q^{ 2 - (\frac{-2}{3}) }= q^{\frac{8}{3}}\\=\sqrt[3]{ q^{8} }=q^{2}.\sqrt[3]{ q^{2} }\\---------------\)
5. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{-1}{2} - (\frac{-1}{3}) }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
6. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{-1}{6}}}\\= y^{ \frac{-1}{3} - (\frac{-1}{6}) }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
7. \(\dfrac{q^{\frac{-1}{5}}}{q^{\frac{1}{3}}}\\= q^{ \frac{-1}{5} - \frac{1}{3} }= q^{\frac{-8}{15}}\\=\frac{1}{\sqrt[15]{ q^{8} }}=\frac{1}{\sqrt[15]{ q^{8} }}. \color{purple}{\frac{\sqrt[15]{ q^{7} }}{\sqrt[15]{ q^{7} }}} \\=\frac{\sqrt[15]{ q^{7} }}{q}\\---------------\)
8. \(\dfrac{x^{\frac{-3}{5}}}{x^{\frac{1}{3}}}\\= x^{ \frac{-3}{5} - \frac{1}{3} }= x^{\frac{-14}{15}}\\=\frac{1}{\sqrt[15]{ x^{14} }}=\frac{1}{\sqrt[15]{ x^{14} }}. \color{purple}{\frac{\sqrt[15]{ x }}{\sqrt[15]{ x }}} \\=\frac{\sqrt[15]{ x }}{x}\\---------------\)
9. \(\dfrac{y^{\frac{-1}{4}}}{y^{\frac{3}{5}}}\\= y^{ \frac{-1}{4} - \frac{3}{5} }= y^{\frac{-17}{20}}\\=\frac{1}{\sqrt[20]{ y^{17} }}=\frac{1}{\sqrt[20]{ y^{17} }}. \color{purple}{\frac{\sqrt[20]{ y^{3} }}{\sqrt[20]{ y^{3} }}} \\=\frac{\sqrt[20]{ y^{3} }}{|y|}\\---------------\)
10. \(\dfrac{y^{\frac{1}{5}}}{y^{\frac{-3}{5}}}\\= y^{ \frac{1}{5} - (\frac{-3}{5}) }= y^{\frac{4}{5}}\\=\sqrt[5]{ y^{4} }\\---------------\)
11. \(\dfrac{a^{\frac{2}{5}}}{a^{-1}}\\= a^{ \frac{2}{5} - (-1) }= a^{\frac{7}{5}}\\=\sqrt[5]{ a^{7} }=a.\sqrt[5]{ a^{2} }\\---------------\)
12. \(\dfrac{q^{\frac{-5}{2}}}{q^{\frac{-5}{4}}}\\= q^{ \frac{-5}{2} - (\frac{-5}{4}) }= q^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ q^{5} }}\\=\frac{1}{|q|.\sqrt[4]{ q }}=\frac{1}{|q|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{2}|}\\---------------\)