Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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