Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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