Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{3}{5}}}{q^{\frac{4}{5}}}\\= q^{ \frac{3}{5} - \frac{4}{5} }= q^{\frac{-1}{5}}\\=\frac{1}{\sqrt[5]{ q }}=\frac{1}{\sqrt[5]{ q }}. \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q}\\---------------\)
2. \(\dfrac{q^{\frac{-5}{3}}}{q^{-1}}\\= q^{ \frac{-5}{3} - (-1) }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
3. \(\dfrac{q^{\frac{-2}{5}}}{q^{\frac{1}{3}}}\\= q^{ \frac{-2}{5} - \frac{1}{3} }= q^{\frac{-11}{15}}\\=\frac{1}{\sqrt[15]{ q^{11} }}=\frac{1}{\sqrt[15]{ q^{11} }}. \color{purple}{\frac{\sqrt[15]{ q^{4} }}{\sqrt[15]{ q^{4} }}} \\=\frac{\sqrt[15]{ q^{4} }}{q}\\---------------\)
4. \(\dfrac{y^{1}}{y^{\frac{2}{5}}}\\= y^{ 1 - \frac{2}{5} }= y^{\frac{3}{5}}\\=\sqrt[5]{ y^{3} }\\---------------\)
5. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{-1}{4}}}\\= q^{ \frac{-2}{3} - (\frac{-1}{4}) }= q^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ q^{5} }}=\frac{1}{\sqrt[12]{ q^{5} }}. \color{purple}{\frac{\sqrt[12]{ q^{7} }}{\sqrt[12]{ q^{7} }}} \\=\frac{\sqrt[12]{ q^{7} }}{|q|}\\---------------\)
6. \(\dfrac{x^{\frac{-3}{4}}}{x^{\frac{1}{6}}}\\= x^{ \frac{-3}{4} - \frac{1}{6} }= x^{\frac{-11}{12}}\\=\frac{1}{\sqrt[12]{ x^{11} }}=\frac{1}{\sqrt[12]{ x^{11} }}. \color{purple}{\frac{\sqrt[12]{ x }}{\sqrt[12]{ x }}} \\=\frac{\sqrt[12]{ x }}{|x|}\\---------------\)
7. \(\dfrac{y^{\frac{4}{5}}}{y^{-1}}\\= y^{ \frac{4}{5} - (-1) }= y^{\frac{9}{5}}\\=\sqrt[5]{ y^{9} }=y.\sqrt[5]{ y^{4} }\\---------------\)
8. \(\dfrac{a^{\frac{-5}{3}}}{a^{\frac{-1}{3}}}\\= a^{ \frac{-5}{3} - (\frac{-1}{3}) }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)
9. \(\dfrac{x^{2}}{x^{\frac{4}{3}}}\\= x^{ 2 - \frac{4}{3} }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
10. \(\dfrac{x^{-1}}{x^{\frac{-4}{3}}}\\= x^{ -1 - (\frac{-4}{3}) }= x^{\frac{1}{3}}\\=\sqrt[3]{ x }\\---------------\)
11. \(\dfrac{a^{\frac{5}{6}}}{a^{\frac{-5}{6}}}\\= a^{ \frac{5}{6} - (\frac{-5}{6}) }= a^{\frac{5}{3}}\\=\sqrt[3]{ a^{5} }=a.\sqrt[3]{ a^{2} }\\---------------\)
12. \(\dfrac{y^{\frac{3}{4}}}{y^{\frac{-2}{5}}}\\= y^{ \frac{3}{4} - (\frac{-2}{5}) }= y^{\frac{23}{20}}\\=\sqrt[20]{ y^{23} }=|y|.\sqrt[20]{ y^{3} }\\---------------\)