Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{1}}{q^{\frac{-3}{5}}}\\= q^{ 1 - (\frac{-3}{5}) }= q^{\frac{8}{5}}\\=\sqrt[5]{ q^{8} }=q.\sqrt[5]{ q^{3} }\\---------------\)
2. \(\dfrac{y^{\frac{-1}{4}}}{y^{\frac{-3}{4}}}\\= y^{ \frac{-1}{4} - (\frac{-3}{4}) }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
3. \(\dfrac{q^{\frac{-1}{2}}}{q^{\frac{5}{6}}}\\= q^{ \frac{-1}{2} - \frac{5}{6} }= q^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ q^{4} }}\\=\frac{1}{q.\sqrt[3]{ q }}=\frac{1}{q.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{2}}\\---------------\)
4. \(\dfrac{x^{\frac{-1}{4}}}{x^{\frac{-5}{4}}}\\= x^{ \frac{-1}{4} - (\frac{-5}{4}) }= x^{1}\\\\---------------\)
5. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{1}{2}}}\\= q^{ \frac{1}{2} - \frac{1}{2} }= q^{0}\\=1\\---------------\)
6. \(\dfrac{q^{\frac{-4}{3}}}{q^{\frac{1}{2}}}\\= q^{ \frac{-4}{3} - \frac{1}{2} }= q^{\frac{-11}{6}}\\=\frac{1}{\sqrt[6]{ q^{11} }}\\=\frac{1}{|q|.\sqrt[6]{ q^{5} }}=\frac{1}{|q|.\sqrt[6]{ q^{5} }} \color{purple}{\frac{\sqrt[6]{ q }}{\sqrt[6]{ q }}} \\=\frac{\sqrt[6]{ q }}{|q^{2}|}\\---------------\)
7. \(\dfrac{x^{\frac{4}{3}}}{x^{\frac{-3}{2}}}\\= x^{ \frac{4}{3} - (\frac{-3}{2}) }= x^{\frac{17}{6}}\\=\sqrt[6]{ x^{17} }=|x^{2}|.\sqrt[6]{ x^{5} }\\---------------\)
8. \(\dfrac{y^{2}}{y^{\frac{-1}{3}}}\\= y^{ 2 - (\frac{-1}{3}) }= y^{\frac{7}{3}}\\=\sqrt[3]{ y^{7} }=y^{2}.\sqrt[3]{ y }\\---------------\)
9. \(\dfrac{q^{\frac{3}{4}}}{q^{\frac{-5}{6}}}\\= q^{ \frac{3}{4} - (\frac{-5}{6}) }= q^{\frac{19}{12}}\\=\sqrt[12]{ q^{19} }=|q|.\sqrt[12]{ q^{7} }\\---------------\)
10. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{4}{3}}}\\= a^{ \frac{2}{3} - \frac{4}{3} }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
11. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{5}{6}}}\\= y^{ \frac{1}{3} - \frac{5}{6} }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
12. \(\dfrac{y^{\frac{4}{3}}}{y^{\frac{5}{6}}}\\= y^{ \frac{4}{3} - \frac{5}{6} }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)