Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-5}{2}}}{a^{\frac{-5}{2}}}\\= a^{ \frac{-5}{2} - (\frac{-5}{2}) }= a^{0}\\=1\\---------------\)
2. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{-1}{6}}}\\= y^{ \frac{-1}{3} - (\frac{-1}{6}) }= y^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ y }}=\frac{1}{\sqrt[6]{ y }}. \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y|}\\---------------\)
3. \(\dfrac{y^{\frac{-5}{6}}}{y^{\frac{-1}{5}}}\\= y^{ \frac{-5}{6} - (\frac{-1}{5}) }= y^{\frac{-19}{30}}\\=\frac{1}{\sqrt[30]{ y^{19} }}=\frac{1}{\sqrt[30]{ y^{19} }}. \color{purple}{\frac{\sqrt[30]{ y^{11} }}{\sqrt[30]{ y^{11} }}} \\=\frac{\sqrt[30]{ y^{11} }}{|y|}\\---------------\)
4. \(\dfrac{y^{\frac{1}{6}}}{y^{\frac{3}{2}}}\\= y^{ \frac{1}{6} - \frac{3}{2} }= y^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ y^{4} }}\\=\frac{1}{y.\sqrt[3]{ y }}=\frac{1}{y.\sqrt[3]{ y }} \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y^{2}}\\---------------\)
5. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{-3}{4}}}\\= x^{ \frac{1}{3} - (\frac{-3}{4}) }= x^{\frac{13}{12}}\\=\sqrt[12]{ x^{13} }=|x|.\sqrt[12]{ x }\\---------------\)
6. \(\dfrac{q^{\frac{3}{2}}}{q^{\frac{-4}{3}}}\\= q^{ \frac{3}{2} - (\frac{-4}{3}) }= q^{\frac{17}{6}}\\=\sqrt[6]{ q^{17} }=|q^{2}|.\sqrt[6]{ q^{5} }\\---------------\)
7. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{-2}{3} - (\frac{-2}{3}) }= q^{0}\\=1\\---------------\)
8. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{3}{5}}}\\= q^{ \frac{1}{4} - \frac{3}{5} }= q^{\frac{-7}{20}}\\=\frac{1}{\sqrt[20]{ q^{7} }}=\frac{1}{\sqrt[20]{ q^{7} }}. \color{purple}{\frac{\sqrt[20]{ q^{13} }}{\sqrt[20]{ q^{13} }}} \\=\frac{\sqrt[20]{ q^{13} }}{|q|}\\---------------\)
9. \(\dfrac{y^{\frac{-4}{3}}}{y^{\frac{-5}{4}}}\\= y^{ \frac{-4}{3} - (\frac{-5}{4}) }= y^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ y }}=\frac{1}{\sqrt[12]{ y }}. \color{purple}{\frac{\sqrt[12]{ y^{11} }}{\sqrt[12]{ y^{11} }}} \\=\frac{\sqrt[12]{ y^{11} }}{|y|}\\---------------\)
10. \(\dfrac{x^{\frac{-5}{6}}}{x^{\frac{5}{4}}}\\= x^{ \frac{-5}{6} - \frac{5}{4} }= x^{\frac{-25}{12}}\\=\frac{1}{\sqrt[12]{ x^{25} }}\\=\frac{1}{|x^{2}|.\sqrt[12]{ x }}=\frac{1}{|x^{2}|.\sqrt[12]{ x }} \color{purple}{\frac{\sqrt[12]{ x^{11} }}{\sqrt[12]{ x^{11} }}} \\=\frac{\sqrt[12]{ x^{11} }}{|x^{3}|}\\---------------\)
11. \(\dfrac{x^{-2}}{x^{\frac{-3}{2}}}\\= x^{ -2 - (\frac{-3}{2}) }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
12. \(\dfrac{q^{1}}{q^{\frac{-3}{5}}}\\= q^{ 1 - (\frac{-3}{5}) }= q^{\frac{8}{5}}\\=\sqrt[5]{ q^{8} }=q.\sqrt[5]{ q^{3} }\\---------------\)