Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{-1}}{q^{-2}}\\= q^{ -1 - (-2) }= q^{1}\\\\---------------\)
2. \(\dfrac{y^{\frac{4}{3}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{4}{3} - (\frac{-1}{3}) }= y^{\frac{5}{3}}\\=\sqrt[3]{ y^{5} }=y.\sqrt[3]{ y^{2} }\\---------------\)
3. \(\dfrac{q^{\frac{3}{4}}}{q^{\frac{-1}{6}}}\\= q^{ \frac{3}{4} - (\frac{-1}{6}) }= q^{\frac{11}{12}}\\=\sqrt[12]{ q^{11} }\\---------------\)
4. \(\dfrac{x^{-1}}{x^{\frac{5}{3}}}\\= x^{ -1 - \frac{5}{3} }= x^{\frac{-8}{3}}\\=\frac{1}{\sqrt[3]{ x^{8} }}\\=\frac{1}{x^{2}.\sqrt[3]{ x^{2} }}=\frac{1}{x^{2}.\sqrt[3]{ x^{2} }} \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x^{3}}\\---------------\)
5. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{2}{5} - (\frac{-2}{3}) }= q^{\frac{16}{15}}\\=\sqrt[15]{ q^{16} }=q.\sqrt[15]{ q }\\---------------\)
6. \(\dfrac{x^{\frac{1}{2}}}{x^{1}}\\= x^{ \frac{1}{2} - 1 }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
7. \(\dfrac{y^{\frac{2}{3}}}{y^{\frac{-1}{6}}}\\= y^{ \frac{2}{3} - (\frac{-1}{6}) }= y^{\frac{5}{6}}\\=\sqrt[6]{ y^{5} }\\---------------\)
8. \(\dfrac{q^{\frac{-4}{3}}}{q^{\frac{5}{4}}}\\= q^{ \frac{-4}{3} - \frac{5}{4} }= q^{\frac{-31}{12}}\\=\frac{1}{\sqrt[12]{ q^{31} }}\\=\frac{1}{|q^{2}|.\sqrt[12]{ q^{7} }}=\frac{1}{|q^{2}|.\sqrt[12]{ q^{7} }} \color{purple}{\frac{\sqrt[12]{ q^{5} }}{\sqrt[12]{ q^{5} }}} \\=\frac{\sqrt[12]{ q^{5} }}{|q^{3}|}\\---------------\)
9. \(\dfrac{y^{\frac{5}{3}}}{y^{\frac{1}{6}}}\\= y^{ \frac{5}{3} - \frac{1}{6} }= y^{\frac{3}{2}}\\= \sqrt{ y^{3} } =|y|. \sqrt{ y } \\---------------\)
10. \(\dfrac{y^{\frac{-1}{5}}}{y^{\frac{-4}{5}}}\\= y^{ \frac{-1}{5} - (\frac{-4}{5}) }= y^{\frac{3}{5}}\\=\sqrt[5]{ y^{3} }\\---------------\)
11. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{-2}{5}}}\\= q^{ \frac{-1}{3} - (\frac{-2}{5}) }= q^{\frac{1}{15}}\\=\sqrt[15]{ q }\\---------------\)
12. \(\dfrac{x^{-2}}{x^{\frac{-5}{2}}}\\= x^{ -2 - (\frac{-5}{2}) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)