Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-3}{5}}}\\= y^{ \frac{-1}{2} - (\frac{-3}{5}) }= y^{\frac{1}{10}}\\=\sqrt[10]{ y }\\---------------\)
2. \(\dfrac{q^{\frac{5}{4}}}{q^{\frac{1}{2}}}\\= q^{ \frac{5}{4} - \frac{1}{2} }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)
3. \(\dfrac{q^{\frac{1}{6}}}{q^{\frac{-1}{5}}}\\= q^{ \frac{1}{6} - (\frac{-1}{5}) }= q^{\frac{11}{30}}\\=\sqrt[30]{ q^{11} }\\---------------\)
4. \(\dfrac{y^{\frac{-4}{5}}}{y^{-1}}\\= y^{ \frac{-4}{5} - (-1) }= y^{\frac{1}{5}}\\=\sqrt[5]{ y }\\---------------\)
5. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{1}{2}}}\\= q^{ \frac{1}{2} - \frac{1}{2} }= q^{0}\\=1\\---------------\)
6. \(\dfrac{x^{\frac{4}{5}}}{x^{\frac{3}{2}}}\\= x^{ \frac{4}{5} - \frac{3}{2} }= x^{\frac{-7}{10}}\\=\frac{1}{\sqrt[10]{ x^{7} }}=\frac{1}{\sqrt[10]{ x^{7} }}. \color{purple}{\frac{\sqrt[10]{ x^{3} }}{\sqrt[10]{ x^{3} }}} \\=\frac{\sqrt[10]{ x^{3} }}{|x|}\\---------------\)
7. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{-4}{3}}}\\= q^{ \frac{2}{5} - (\frac{-4}{3}) }= q^{\frac{26}{15}}\\=\sqrt[15]{ q^{26} }=q.\sqrt[15]{ q^{11} }\\---------------\)
8. \(\dfrac{q^{\frac{-1}{4}}}{q^{\frac{-5}{4}}}\\= q^{ \frac{-1}{4} - (\frac{-5}{4}) }= q^{1}\\\\---------------\)
9. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{-5}{4}}}\\= q^{ \frac{-1}{2} - (\frac{-5}{4}) }= q^{\frac{3}{4}}\\=\sqrt[4]{ q^{3} }\\---------------\)
10. \(\dfrac{q^{\frac{-5}{6}}}{q^{\frac{-3}{5}}}\\= q^{ \frac{-5}{6} - (\frac{-3}{5}) }= q^{\frac{-7}{30}}\\=\frac{1}{\sqrt[30]{ q^{7} }}=\frac{1}{\sqrt[30]{ q^{7} }}. \color{purple}{\frac{\sqrt[30]{ q^{23} }}{\sqrt[30]{ q^{23} }}} \\=\frac{\sqrt[30]{ q^{23} }}{|q|}\\---------------\)
11. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{1}{2}}}\\= x^{ \frac{1}{3} - \frac{1}{2} }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
12. \(\dfrac{y^{\frac{1}{4}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{1}{4} - (\frac{-1}{3}) }= y^{\frac{7}{12}}\\=\sqrt[12]{ y^{7} }\\---------------\)