Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{1}{6}}}{x^{\frac{1}{2}}}\\= x^{ \frac{1}{6} - \frac{1}{2} }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
2. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{-3}{5}}}\\= q^{ \frac{1}{2} - (\frac{-3}{5}) }= q^{\frac{11}{10}}\\=\sqrt[10]{ q^{11} }=|q|.\sqrt[10]{ q }\\---------------\)
3. \(\dfrac{y^{1}}{y^{\frac{1}{3}}}\\= y^{ 1 - \frac{1}{3} }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
4. \(\dfrac{a^{\frac{1}{5}}}{a^{\frac{1}{2}}}\\= a^{ \frac{1}{5} - \frac{1}{2} }= a^{\frac{-3}{10}}\\=\frac{1}{\sqrt[10]{ a^{3} }}=\frac{1}{\sqrt[10]{ a^{3} }}. \color{purple}{\frac{\sqrt[10]{ a^{7} }}{\sqrt[10]{ a^{7} }}} \\=\frac{\sqrt[10]{ a^{7} }}{|a|}\\---------------\)
5. \(\dfrac{x^{\frac{1}{5}}}{x^{\frac{1}{5}}}\\= x^{ \frac{1}{5} - \frac{1}{5} }= x^{0}\\=1\\---------------\)
6. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{4}{3}}}\\= q^{ \frac{-1}{2} - \frac{4}{3} }= q^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ q^{11} }}\\=\frac{1}{|q|.\sqrt[6]{ q^{5} }}=\frac{1}{|q|.\sqrt[6]{ q^{5} }} \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q^{2}|}\\---------------\)
7. \(\dfrac{y^{\frac{-4}{5}}}{y^{\frac{-3}{5}}}\\= y^{ \frac{-4}{5} - (\frac{-3}{5}) }= y^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ y }}=\frac{1}{\sqrt[5]{ y }}. \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y}\\---------------\)
8. \(\dfrac{q^{\frac{4}{5}}}{q^{\frac{1}{2}}}\\= q^{ \frac{4}{5} - \frac{1}{2} }= q^{\frac{3}{10}}\\=\sqrt[10]{ q^{3} }\\---------------\)
9. \(\dfrac{x^{\frac{-1}{2}}}{x^{-1}}\\= x^{ \frac{-1}{2} - (-1) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
10. \(\dfrac{a^{1}}{a^{\frac{-2}{5}}}\\= a^{ 1 - (\frac{-2}{5}) }= a^{\frac{7}{5}}\\=\sqrt[5]{ a^{7} }=a.\sqrt[5]{ a^{2} }\\---------------\)
11. \(\dfrac{a^{\frac{1}{6}}}{a^{\frac{5}{4}}}\\= a^{ \frac{1}{6} - \frac{5}{4} }= a^{\frac{-13}{12}}\\=\frac{1}{\sqrt[12]{ a^{13} }}\\=\frac{1}{|a|.\sqrt[12]{ a }}=\frac{1}{|a|.\sqrt[12]{ a }} \color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a^{2}|}\\---------------\)
12. \(\dfrac{y^{-2}}{y^{\frac{-1}{4}}}\\= y^{ -2 - (\frac{-1}{4}) }= y^{\frac{-7}{4}}\\=\frac{1}{\sqrt[4]{ y^{7} }}\\=\frac{1}{|y|.\sqrt[4]{ y^{3} }}=\frac{1}{|y|.\sqrt[4]{ y^{3} }} \color{purple}{\frac{\sqrt[4]{ y }}{\sqrt[4]{ y }}} \\=\frac{\sqrt[4]{ y }}{|y^{2}|}\\---------------\)