Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-4}{3}}}{y^{\frac{-5}{6}}}\\= y^{ \frac{-4}{3} - (\frac{-5}{6}) }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
2. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{3}{2}}}\\= q^{ \frac{1}{3} - \frac{3}{2} }= q^{\frac{-7}{6}}\\=\frac{1}{\sqrt[6]{ q^{7} }}\\=\frac{1}{|q|.\sqrt[6]{ q }}=\frac{1}{|q|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{2}|}\\---------------\)
3. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{-1}{5}}}\\= a^{ \frac{2}{3} - (\frac{-1}{5}) }= a^{\frac{13}{15}}\\=\sqrt[15]{ a^{13} }\\---------------\)
4. \(\dfrac{y^{\frac{3}{4}}}{y^{\frac{4}{5}}}\\= y^{ \frac{3}{4} - \frac{4}{5} }= y^{\frac{-1}{20}}\\=\frac{1}{\sqrt[20]{ y }}=\frac{1}{\sqrt[20]{ y }}. \color{purple}{\frac{\sqrt[20]{ y^{19} }}{\sqrt[20]{ y^{19} }}} \\=\frac{\sqrt[20]{ y^{19} }}{|y|}\\---------------\)
5. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{-2}{3} - (\frac{-1}{3}) }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
6. \(\dfrac{a^{\frac{3}{5}}}{a^{\frac{-1}{5}}}\\= a^{ \frac{3}{5} - (\frac{-1}{5}) }= a^{\frac{4}{5}}\\=\sqrt[5]{ a^{4} }\\---------------\)
7. \(\dfrac{a^{\frac{1}{4}}}{a^{\frac{-3}{5}}}\\= a^{ \frac{1}{4} - (\frac{-3}{5}) }= a^{\frac{17}{20}}\\=\sqrt[20]{ a^{17} }\\---------------\)
8. \(\dfrac{x^{\frac{5}{4}}}{x^{\frac{5}{2}}}\\= x^{ \frac{5}{4} - \frac{5}{2} }= x^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ x^{5} }}\\=\frac{1}{|x|.\sqrt[4]{ x }}=\frac{1}{|x|.\sqrt[4]{ x }} \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x^{2}|}\\---------------\)
9. \(\dfrac{q^{\frac{1}{6}}}{q^{\frac{1}{2}}}\\= q^{ \frac{1}{6} - \frac{1}{2} }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
10. \(\dfrac{q^{1}}{q^{\frac{-4}{3}}}\\= q^{ 1 - (\frac{-4}{3}) }= q^{\frac{7}{3}}\\=\sqrt[3]{ q^{7} }=q^{2}.\sqrt[3]{ q }\\---------------\)
11. \(\dfrac{a^{\frac{1}{4}}}{a^{\frac{2}{3}}}\\= a^{ \frac{1}{4} - \frac{2}{3} }= a^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ a^{5} }}=\frac{1}{\sqrt[12]{ a^{5} }}. \color{purple}{\frac{\sqrt[12]{ a^{7} }}{\sqrt[12]{ a^{7} }}} \\=\frac{\sqrt[12]{ a^{7} }}{|a|}\\---------------\)
12. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{1}{3} - (\frac{-1}{3}) }= y^{\frac{2}{3}}\\=\sqrt[3]{ y^{2} }\\---------------\)