Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{2}{3} - (\frac{-1}{2}) }= q^{\frac{7}{6}}\\=\sqrt[6]{ q^{7} }=|q|.\sqrt[6]{ q }\\---------------\)
2. \(\dfrac{y^{-1}}{y^{\frac{-1}{4}}}\\= y^{ -1 - (\frac{-1}{4}) }= y^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ y^{3} }}=\frac{1}{\sqrt[4]{ y^{3} }}. \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y|}\\---------------\)
3. \(\dfrac{a^{\frac{-5}{2}}}{a^{\frac{4}{5}}}\\= a^{ \frac{-5}{2} - \frac{4}{5} }= a^{\frac{-33}{10}}\\=\frac{1}{\sqrt[10]{ a^{33} }}\\=\frac{1}{|a^{3}|.\sqrt[10]{ a^{3} }}=\frac{1}{|a^{3}|.\sqrt[10]{ a^{3} }} \color{purple}{\frac{\sqrt[10]{ a^{7} }}{\sqrt[10]{ a^{7} }}} \\=\frac{\sqrt[10]{ a^{7} }}{|a^{4}|}\\---------------\)
4. \(\dfrac{x^{\frac{1}{4}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{1}{4} - (\frac{-1}{2}) }= x^{\frac{3}{4}}\\=\sqrt[4]{ x^{3} }\\---------------\)
5. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{4}{5}}}\\= q^{ \frac{2}{3} - \frac{4}{5} }= q^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ q^{2} }}=\frac{1}{\sqrt[15]{ q^{2} }}. \color{purple}{\frac{\sqrt[15]{ q^{13} }}{\sqrt[15]{ q^{13} }}} \\=\frac{\sqrt[15]{ q^{13} }}{q}\\---------------\)
6. \(\dfrac{x^{\frac{-3}{4}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{-3}{4} - (\frac{-2}{3}) }= x^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ x }}=\frac{1}{\sqrt[12]{ x }}. \color{purple}{\frac{\sqrt[12]{ x^{11} }}{\sqrt[12]{ x^{11} }}} \\=\frac{\sqrt[12]{ x^{11} }}{|x|}\\---------------\)
7. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-5}{2}}}\\= a^{ \frac{-1}{2} - (\frac{-5}{2}) }= a^{2}\\\\---------------\)
8. \(\dfrac{y^{1}}{y^{\frac{1}{6}}}\\= y^{ 1 - \frac{1}{6} }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
9. \(\dfrac{a^{\frac{5}{2}}}{a^{\frac{1}{6}}}\\= a^{ \frac{5}{2} - \frac{1}{6} }= a^{\frac{7}{3}}\\=\sqrt[3]{ a^{7} }=a^{2}.\sqrt[3]{ a }\\---------------\)
10. \(\dfrac{y^{-2}}{y^{\frac{4}{5}}}\\= y^{ -2 - \frac{4}{5} }= y^{\frac{-14}{5}}\\=\frac{1}{\sqrt[5]{ y^{14} }}\\=\frac{1}{y^{2}.\sqrt[5]{ y^{4} }}=\frac{1}{y^{2}.\sqrt[5]{ y^{4} }} \color{purple}{\frac{\sqrt[5]{ y }}{\sqrt[5]{ y }}} \\=\frac{\sqrt[5]{ y }}{y^{3}}\\---------------\)
11. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-1}{2} - \frac{1}{2} }= q^{-1}\\=\frac{1}{q}\\---------------\)
12. \(\dfrac{a^{\frac{-2}{5}}}{a^{1}}\\= a^{ \frac{-2}{5} - 1 }= a^{\frac{-7}{5}}\\=\frac{1}{\sqrt[5]{ a^{7} }}\\=\frac{1}{a.\sqrt[5]{ a^{2} }}=\frac{1}{a.\sqrt[5]{ a^{2} }} \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a^{2}}\\---------------\)