Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-5}{3}}}{y^{\frac{5}{6}}}\\= y^{ \frac{-5}{3} - \frac{5}{6} }= y^{\frac{-5}{2}}\\=\frac{1}{ \sqrt{ y^{5} } }\\=\frac{1}{|y^{2}|. \sqrt{ y } }=\frac{1}{|y^{2}|. \sqrt{ y } } \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y^{3}|}\\---------------\)
2. \(\dfrac{a^{1}}{a^{\frac{5}{3}}}\\= a^{ 1 - \frac{5}{3} }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
3. \(\dfrac{x^{\frac{3}{5}}}{x^{\frac{-1}{2}}}\\= x^{ \frac{3}{5} - (\frac{-1}{2}) }= x^{\frac{11}{10}}\\=\sqrt[10]{ x^{11} }=|x|.\sqrt[10]{ x }\\---------------\)
4. \(\dfrac{q^{\frac{-3}{2}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{-3}{2} - (\frac{-1}{2}) }= q^{-1}\\=\frac{1}{q}\\---------------\)
5. \(\dfrac{q^{\frac{3}{4}}}{q^{1}}\\= q^{ \frac{3}{4} - 1 }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)
6. \(\dfrac{q^{\frac{3}{2}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{3}{2} - (\frac{-2}{3}) }= q^{\frac{13}{6}}\\=\sqrt[6]{ q^{13} }=|q^{2}|.\sqrt[6]{ q }\\---------------\)
7. \(\dfrac{y^{-1}}{y^{\frac{1}{5}}}\\= y^{ -1 - \frac{1}{5} }= y^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ y^{6} }}\\=\frac{1}{y.\sqrt[5]{ y }}=\frac{1}{y.\sqrt[5]{ y }} \color{purple}{\frac{\sqrt[5]{ y^{4} }}{\sqrt[5]{ y^{4} }}} \\=\frac{\sqrt[5]{ y^{4} }}{y^{2}}\\---------------\)
8. \(\dfrac{y^{\frac{5}{4}}}{y^{\frac{-4}{5}}}\\= y^{ \frac{5}{4} - (\frac{-4}{5}) }= y^{\frac{41}{20}}\\=\sqrt[20]{ y^{41} }=|y^{2}|.\sqrt[20]{ y }\\---------------\)
9. \(\dfrac{y^{\frac{1}{2}}}{y^{\frac{-1}{4}}}\\= y^{ \frac{1}{2} - (\frac{-1}{4}) }= y^{\frac{3}{4}}\\=\sqrt[4]{ y^{3} }\\---------------\)
10. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{5}{2}}}\\= y^{ \frac{-1}{3} - \frac{5}{2} }= y^{\frac{-17}{6}}\\=\frac{1}{\sqrt[6]{ y^{17} }}\\=\frac{1}{|y^{2}|.\sqrt[6]{ y^{5} }}=\frac{1}{|y^{2}|.\sqrt[6]{ y^{5} }} \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y^{3}|}\\---------------\)
11. \(\dfrac{a^{\frac{-1}{2}}}{a^{\frac{-5}{3}}}\\= a^{ \frac{-1}{2} - (\frac{-5}{3}) }= a^{\frac{7}{6}}\\=\sqrt[6]{ a^{7} }=|a|.\sqrt[6]{ a }\\---------------\)
12. \(\dfrac{y^{\frac{-2}{3}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{-2}{3} - (\frac{-1}{3}) }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)