Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{a^{\frac{-1}{3}}}{a^{\frac{3}{4}}}\\= a^{ \frac{-1}{3} - \frac{3}{4} }= a^{\frac{-13}{12}}\\=\frac{1}{\sqrt[12]{ a^{13} }}\\=\frac{1}{|a|.\sqrt[12]{ a }}=\frac{1}{|a|.\sqrt[12]{ a }} \color{purple}{\frac{\sqrt[12]{ a^{11} }}{\sqrt[12]{ a^{11} }}} \\=\frac{\sqrt[12]{ a^{11} }}{|a^{2}|}\\---------------\)
2. \(\dfrac{y^{-2}}{y^{\frac{4}{5}}}\\= y^{ -2 - \frac{4}{5} }= y^{\frac{-14}{5}}\\=\frac{1}{\sqrt[5]{ y^{14} }}\\=\frac{1}{y^{2}.\sqrt[5]{ y^{4} }}=\frac{1}{y^{2}.\sqrt[5]{ y^{4} }} \color{purple}{\frac{\sqrt[5]{ y }}{\sqrt[5]{ y }}} \\=\frac{\sqrt[5]{ y }}{y^{3}}\\---------------\)
3. \(\dfrac{q^{\frac{1}{4}}}{q^{\frac{3}{2}}}\\= q^{ \frac{1}{4} - \frac{3}{2} }= q^{\frac{-5}{4}}\\=\frac{1}{\sqrt[4]{ q^{5} }}\\=\frac{1}{|q|.\sqrt[4]{ q }}=\frac{1}{|q|.\sqrt[4]{ q }} \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q^{2}|}\\---------------\)
4. \(\dfrac{x^{\frac{2}{3}}}{x^{\frac{3}{4}}}\\= x^{ \frac{2}{3} - \frac{3}{4} }= x^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ x }}=\frac{1}{\sqrt[12]{ x }}. \color{purple}{\frac{\sqrt[12]{ x^{11} }}{\sqrt[12]{ x^{11} }}} \\=\frac{\sqrt[12]{ x^{11} }}{|x|}\\---------------\)
5. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{2}{3}}}\\= q^{ \frac{1}{3} - \frac{2}{3} }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
6. \(\dfrac{q^{-1}}{q^{-1}}\\= q^{ -1 - (-1) }= q^{0}\\=1\\---------------\)
7. \(\dfrac{x^{\frac{1}{5}}}{x^{1}}\\= x^{ \frac{1}{5} - 1 }= x^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ x^{4} }}=\frac{1}{\sqrt[5]{ x^{4} }}. \color{purple}{\frac{\sqrt[5]{ x }}{\sqrt[5]{ x }}} \\=\frac{\sqrt[5]{ x }}{x}\\---------------\)
8. \(\dfrac{y^{\frac{1}{2}}}{y^{1}}\\= y^{ \frac{1}{2} - 1 }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
9. \(\dfrac{a^{-2}}{a^{\frac{-5}{4}}}\\= a^{ -2 - (\frac{-5}{4}) }= a^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ a^{3} }}=\frac{1}{\sqrt[4]{ a^{3} }}. \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a|}\\---------------\)
10. \(\dfrac{a^{\frac{-1}{6}}}{a^{\frac{-2}{3}}}\\= a^{ \frac{-1}{6} - (\frac{-2}{3}) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
11. \(\dfrac{q^{\frac{-1}{4}}}{q^{\frac{-3}{5}}}\\= q^{ \frac{-1}{4} - (\frac{-3}{5}) }= q^{\frac{7}{20}}\\=\sqrt[20]{ q^{7} }\\---------------\)
12. \(\dfrac{x^{\frac{-1}{4}}}{x^{\frac{3}{5}}}\\= x^{ \frac{-1}{4} - \frac{3}{5} }= x^{\frac{-17}{20}}\\=\frac{1}{\sqrt[20]{ x^{17} }}=\frac{1}{\sqrt[20]{ x^{17} }}. \color{purple}{\frac{\sqrt[20]{ x^{3} }}{\sqrt[20]{ x^{3} }}} \\=\frac{\sqrt[20]{ x^{3} }}{|x|}\\---------------\)