Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-5}{2}}}{q^{\frac{5}{2}}}\\= q^{ \frac{-5}{2} - \frac{5}{2} }= q^{-5}\\=\frac{1}{q^{5}}\\---------------\)
2. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{3}{2}}}\\= q^{ \frac{2}{3} - \frac{3}{2} }= q^{\frac{-5}{6}}\\=\frac{1}{\sqrt[6]{ q^{5} }}=\frac{1}{\sqrt[6]{ q^{5} }}. \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q|}\\---------------\)
3. \(\dfrac{x^{\frac{1}{6}}}{x^{\frac{-5}{3}}}\\= x^{ \frac{1}{6} - (\frac{-5}{3}) }= x^{\frac{11}{6}}\\=\sqrt[6]{ x^{11} }=|x|.\sqrt[6]{ x^{5} }\\---------------\)
4. \(\dfrac{q^{-2}}{q^{\frac{3}{4}}}\\= q^{ -2 - \frac{3}{4} }= q^{\frac{-11}{4}}\\=\frac{1}{\sqrt[4]{ q^{11} }}\\=\frac{1}{|q^{2}|.\sqrt[4]{ q^{3} }}=\frac{1}{|q^{2}|.\sqrt[4]{ q^{3} }} \color{purple}{\frac{\sqrt[4]{ q }}{\sqrt[4]{ q }}} \\=\frac{\sqrt[4]{ q }}{|q^{3}|}\\---------------\)
5. \(\dfrac{y^{1}}{y^{1}}\\= y^{ 1 - 1 }= y^{0}\\=1\\---------------\)
6. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{-5}{3}}}\\= x^{ \frac{2}{3} - (\frac{-5}{3}) }= x^{\frac{7}{3}}\\=\sqrt[3]{ x^{7} }=x^{2}.\sqrt[3]{ x }\\---------------\)
7. \(\dfrac{a^{\frac{5}{4}}}{a^{\frac{-5}{6}}}\\= a^{ \frac{5}{4} - (\frac{-5}{6}) }= a^{\frac{25}{12}}\\=\sqrt[12]{ a^{25} }=|a^{2}|.\sqrt[12]{ a }\\---------------\)
8. \(\dfrac{q^{\frac{5}{4}}}{q^{\frac{1}{5}}}\\= q^{ \frac{5}{4} - \frac{1}{5} }= q^{\frac{21}{20}}\\=\sqrt[20]{ q^{21} }=|q|.\sqrt[20]{ q }\\---------------\)
9. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{-3}{4}}}\\= y^{ \frac{5}{2} - (\frac{-3}{4}) }= y^{\frac{13}{4}}\\=\sqrt[4]{ y^{13} }=|y^{3}|.\sqrt[4]{ y }\\---------------\)
10. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-5}{2}}}\\= y^{ \frac{1}{2} - (\frac{-5}{2}) }= y^{3}\\\\---------------\)
11. \(\dfrac{a^{-1}}{a^{\frac{1}{3}}}\\= a^{ -1 - \frac{1}{3} }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)
12. \(\dfrac{y^{\frac{5}{6}}}{y^{\frac{-3}{2}}}\\= y^{ \frac{5}{6} - (\frac{-3}{2}) }= y^{\frac{7}{3}}\\=\sqrt[3]{ y^{7} }=y^{2}.\sqrt[3]{ y }\\---------------\)