Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{-1}}{q^{\frac{-1}{3}}}\\= q^{ -1 - (\frac{-1}{3}) }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
2. \(\dfrac{y^{\frac{-3}{2}}}{y^{-1}}\\= y^{ \frac{-3}{2} - (-1) }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
3. \(\dfrac{q^{\frac{4}{3}}}{q^{-2}}\\= q^{ \frac{4}{3} - (-2) }= q^{\frac{10}{3}}\\=\sqrt[3]{ q^{10} }=q^{3}.\sqrt[3]{ q }\\---------------\)
4. \(\dfrac{x^{-1}}{x^{1}}\\= x^{ -1 - 1 }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
5. \(\dfrac{x^{\frac{5}{6}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{5}{6} - (\frac{-1}{2}) }= x^{\frac{4}{3}}\\=\sqrt[3]{ x^{4} }=x.\sqrt[3]{ x }\\---------------\)
6. \(\dfrac{x^{\frac{1}{5}}}{x^{\frac{1}{4}}}\\= x^{ \frac{1}{5} - \frac{1}{4} }= x^{\frac{-1}{20}}\\=\frac{1}{\sqrt[20]{ x }}=\frac{1}{\sqrt[20]{ x }}. \color{purple}{\frac{\sqrt[20]{ x^{19} }}{\sqrt[20]{ x^{19} }}} \\=\frac{\sqrt[20]{ x^{19} }}{|x|}\\---------------\)
7. \(\dfrac{x^{\frac{-1}{3}}}{x^{1}}\\= x^{ \frac{-1}{3} - 1 }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
8. \(\dfrac{y^{\frac{-5}{2}}}{y^{\frac{3}{2}}}\\= y^{ \frac{-5}{2} - \frac{3}{2} }= y^{-4}\\=\frac{1}{y^{4}}\\---------------\)
9. \(\dfrac{a^{\frac{3}{5}}}{a^{\frac{-1}{4}}}\\= a^{ \frac{3}{5} - (\frac{-1}{4}) }= a^{\frac{17}{20}}\\=\sqrt[20]{ a^{17} }\\---------------\)
10. \(\dfrac{q^{\frac{3}{5}}}{q^{\frac{1}{2}}}\\= q^{ \frac{3}{5} - \frac{1}{2} }= q^{\frac{1}{10}}\\=\sqrt[10]{ q }\\---------------\)
11. \(\dfrac{q^{\frac{5}{6}}}{q^{\frac{4}{5}}}\\= q^{ \frac{5}{6} - \frac{4}{5} }= q^{\frac{1}{30}}\\=\sqrt[30]{ q }\\---------------\)
12. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{2}{3}}}\\= a^{ \frac{-1}{3} - \frac{2}{3} }= a^{-1}\\=\frac{1}{a}\\---------------\)