Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{1}{6}}}{q^{\frac{1}{2}}}\\= q^{ \frac{1}{6} - \frac{1}{2} }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
2. \(\dfrac{y^{\frac{4}{3}}}{y^{\frac{2}{3}}}\\= y^{ \frac{4}{3} - \frac{2}{3} }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)
3. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{5}{6}}}\\= x^{ \frac{-1}{2} - \frac{5}{6} }= x^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ x^{4} }}\\=\frac{1}{x.\sqrt[3]{ x }}=\frac{1}{x.\sqrt[3]{ x }} \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x^{2}}\\---------------\)
4. \(\dfrac{a^{\frac{1}{5}}}{a^{\frac{3}{5}}}\\= a^{ \frac{1}{5} - \frac{3}{5} }= a^{\frac{-2}{5}}\\=\frac{1}{\sqrt[5]{ a^{2} }}=\frac{1}{\sqrt[5]{ a^{2} }}. \color{purple}{\frac{\sqrt[5]{ a^{3} }}{\sqrt[5]{ a^{3} }}} \\=\frac{\sqrt[5]{ a^{3} }}{a}\\---------------\)
5. \(\dfrac{x^{\frac{3}{4}}}{x^{\frac{2}{3}}}\\= x^{ \frac{3}{4} - \frac{2}{3} }= x^{\frac{1}{12}}\\=\sqrt[12]{ x }\\---------------\)
6. \(\dfrac{q^{\frac{-5}{6}}}{q^{-1}}\\= q^{ \frac{-5}{6} - (-1) }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
7. \(\dfrac{y^{1}}{y^{\frac{-2}{3}}}\\= y^{ 1 - (\frac{-2}{3}) }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)
8. \(\dfrac{x^{\frac{-1}{6}}}{x^{\frac{-3}{5}}}\\= x^{ \frac{-1}{6} - (\frac{-3}{5}) }= x^{\frac{13}{30}}\\=\sqrt[30]{ x^{13} }\\---------------\)
9. \(\dfrac{a^{\frac{-3}{2}}}{a^{\frac{3}{2}}}\\= a^{ \frac{-3}{2} - \frac{3}{2} }= a^{-3}\\=\frac{1}{a^{3}}\\---------------\)
10. \(\dfrac{x^{-1}}{x^{1}}\\= x^{ -1 - 1 }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
11. \(\dfrac{y^{1}}{y^{\frac{3}{2}}}\\= y^{ 1 - \frac{3}{2} }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
12. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{-1}{3} - (\frac{-1}{2}) }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)