Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{3}{5}}}{q^{\frac{5}{4}}}\\= q^{ \frac{3}{5} - \frac{5}{4} }= q^{\frac{-13}{20}}\\=\frac{1}{\sqrt[20]{ q^{13} }}=\frac{1}{\sqrt[20]{ q^{13} }}. \color{purple}{\frac{\sqrt[20]{ q^{7} }}{\sqrt[20]{ q^{7} }}} \\=\frac{\sqrt[20]{ q^{7} }}{|q|}\\---------------\)
2. \(\dfrac{a^{-1}}{a^{\frac{-5}{4}}}\\= a^{ -1 - (\frac{-5}{4}) }= a^{\frac{1}{4}}\\=\sqrt[4]{ a }\\---------------\)
3. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{5}{3}}}\\= q^{ \frac{-2}{3} - \frac{5}{3} }= q^{\frac{-7}{3}}\\=\frac{1}{\sqrt[3]{ q^{7} }}\\=\frac{1}{q^{2}.\sqrt[3]{ q }}=\frac{1}{q^{2}.\sqrt[3]{ q }} \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q^{3}}\\---------------\)
4. \(\dfrac{a^{\frac{1}{6}}}{a^{\frac{-1}{4}}}\\= a^{ \frac{1}{6} - (\frac{-1}{4}) }= a^{\frac{5}{12}}\\=\sqrt[12]{ a^{5} }\\---------------\)
5. \(\dfrac{x^{\frac{3}{4}}}{x^{1}}\\= x^{ \frac{3}{4} - 1 }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
6. \(\dfrac{x^{\frac{-4}{5}}}{x^{\frac{2}{3}}}\\= x^{ \frac{-4}{5} - \frac{2}{3} }= x^{\frac{-22}{15}}\\=\frac{1}{\sqrt[15]{ x^{22} }}\\=\frac{1}{x.\sqrt[15]{ x^{7} }}=\frac{1}{x.\sqrt[15]{ x^{7} }} \color{purple}{\frac{\sqrt[15]{ x^{8} }}{\sqrt[15]{ x^{8} }}} \\=\frac{\sqrt[15]{ x^{8} }}{x^{2}}\\---------------\)
7. \(\dfrac{a^{-1}}{a^{\frac{-2}{3}}}\\= a^{ -1 - (\frac{-2}{3}) }= a^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ a }}=\frac{1}{\sqrt[3]{ a }}. \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a}\\---------------\)
8. \(\dfrac{y^{\frac{-1}{5}}}{y^{-1}}\\= y^{ \frac{-1}{5} - (-1) }= y^{\frac{4}{5}}\\=\sqrt[5]{ y^{4} }\\---------------\)
9. \(\dfrac{x^{-1}}{x^{\frac{-3}{4}}}\\= x^{ -1 - (\frac{-3}{4}) }= x^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ x }}=\frac{1}{\sqrt[4]{ x }}. \color{purple}{\frac{\sqrt[4]{ x^{3} }}{\sqrt[4]{ x^{3} }}} \\=\frac{\sqrt[4]{ x^{3} }}{|x|}\\---------------\)
10. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{5}{3}}}\\= a^{ \frac{1}{3} - \frac{5}{3} }= a^{\frac{-4}{3}}\\=\frac{1}{\sqrt[3]{ a^{4} }}\\=\frac{1}{a.\sqrt[3]{ a }}=\frac{1}{a.\sqrt[3]{ a }} \color{purple}{\frac{\sqrt[3]{ a^{2} }}{\sqrt[3]{ a^{2} }}} \\=\frac{\sqrt[3]{ a^{2} }}{a^{2}}\\---------------\)
11. \(\dfrac{y^{\frac{3}{4}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{3}{4} - (\frac{-1}{2}) }= y^{\frac{5}{4}}\\=\sqrt[4]{ y^{5} }=|y|.\sqrt[4]{ y }\\---------------\)
12. \(\dfrac{q^{\frac{-3}{2}}}{q^{2}}\\= q^{ \frac{-3}{2} - 2 }= q^{\frac{-7}{2}}\\=\frac{1}{ \sqrt{ q^{7} } }\\=\frac{1}{|q^{3}|. \sqrt{ q } }=\frac{1}{|q^{3}|. \sqrt{ q } } \color{purple}{\frac{ \sqrt{ q } }{ \sqrt{ q } }} \\=\frac{ \sqrt{ q } }{|q^{4}|}\\---------------\)