Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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