Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-5}{4}}}{x^{-2}}\\= x^{ \frac{-5}{4} - (-2) }= x^{\frac{3}{4}}\\=\sqrt[4]{ x^{3} }\\---------------\)
2. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{4}{3}}}\\= q^{ \frac{1}{4} - \frac{4}{3} }= q^{\frac{-13}{12}}\\=\frac{1}{\sqrt[12]{ q^{13} }}\\=\frac{1}{|q|.\sqrt[12]{ q }}=\frac{1}{|q|.\sqrt[12]{ q }} \color{purple}{\frac{\sqrt[12]{ q^{11} }}{\sqrt[12]{ q^{11} }}} \\=\frac{\sqrt[12]{ q^{11} }}{|q^{2}|}\\---------------\)
3. \(\dfrac{q^{\frac{-5}{3}}}{q^{-1}}\\= q^{ \frac{-5}{3} - (-1) }= q^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ q^{2} }}=\frac{1}{\sqrt[3]{ q^{2} }}. \color{purple}{\frac{\sqrt[3]{ q }}{\sqrt[3]{ q }}} \\=\frac{\sqrt[3]{ q }}{q}\\---------------\)
4. \(\dfrac{q^{\frac{-1}{6}}}{q^{\frac{-1}{6}}}\\= q^{ \frac{-1}{6} - (\frac{-1}{6}) }= q^{0}\\=1\\---------------\)
5. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{1}{6}}}\\= y^{ \frac{-1}{3} - \frac{1}{6} }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
6. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{-4}{3}}}\\= q^{ \frac{2}{3} - (\frac{-4}{3}) }= q^{2}\\\\---------------\)
7. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{5}{2}}}\\= a^{ \frac{1}{3} - \frac{5}{2} }= a^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ a^{13} }}\\=\frac{1}{|a^{2}|.\sqrt[6]{ a }}=\frac{1}{|a^{2}|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{3}|}\\---------------\)
8. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-2}{5}}}\\= y^{ \frac{-1}{2} - (\frac{-2}{5}) }= y^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ y }}=\frac{1}{\sqrt[10]{ y }}. \color{purple}{\frac{\sqrt[10]{ y^{9} }}{\sqrt[10]{ y^{9} }}} \\=\frac{\sqrt[10]{ y^{9} }}{|y|}\\---------------\)
9. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{-2}{5}}}\\= q^{ \frac{-1}{3} - (\frac{-2}{5}) }= q^{\frac{1}{15}}\\=\sqrt[15]{ q }\\---------------\)
10. \(\dfrac{x^{-1}}{x^{\frac{-2}{5}}}\\= x^{ -1 - (\frac{-2}{5}) }= x^{\frac{-3}{5}}\\=\frac{1}{\sqrt[5]{ x^{3} }}=\frac{1}{\sqrt[5]{ x^{3} }}. \color{purple}{\frac{\sqrt[5]{ x^{2} }}{\sqrt[5]{ x^{2} }}} \\=\frac{\sqrt[5]{ x^{2} }}{x}\\---------------\)
11. \(\dfrac{y^{\frac{-5}{2}}}{y^{\frac{-1}{2}}}\\= y^{ \frac{-5}{2} - (\frac{-1}{2}) }= y^{-2}\\=\frac{1}{y^{2}}\\---------------\)
12. \(\dfrac{a^{\frac{-5}{3}}}{a^{\frac{1}{5}}}\\= a^{ \frac{-5}{3} - \frac{1}{5} }= a^{\frac{-28}{15}}\\=\frac{1}{\sqrt[15]{ a^{28} }}\\=\frac{1}{a.\sqrt[15]{ a^{13} }}=\frac{1}{a.\sqrt[15]{ a^{13} }} \color{purple}{\frac{\sqrt[15]{ a^{2} }}{\sqrt[15]{ a^{2} }}} \\=\frac{\sqrt[15]{ a^{2} }}{a^{2}}\\---------------\)