Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{1}{3}}}{y^{\frac{5}{6}}}\\= y^{ \frac{1}{3} - \frac{5}{6} }= y^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ y } }=\frac{1}{ \sqrt{ y } }. \color{purple}{\frac{ \sqrt{ y } }{ \sqrt{ y } }} \\=\frac{ \sqrt{ y } }{|y|}\\---------------\)
2. \(\dfrac{a^{-1}}{a^{\frac{4}{5}}}\\= a^{ -1 - \frac{4}{5} }= a^{\frac{-9}{5}}\\=\frac{1}{\sqrt[5]{ a^{9} }}\\=\frac{1}{a.\sqrt[5]{ a^{4} }}=\frac{1}{a.\sqrt[5]{ a^{4} }} \color{purple}{\frac{\sqrt[5]{ a }}{\sqrt[5]{ a }}} \\=\frac{\sqrt[5]{ a }}{a^{2}}\\---------------\)
3. \(\dfrac{x^{\frac{5}{6}}}{x^{\frac{3}{2}}}\\= x^{ \frac{5}{6} - \frac{3}{2} }= x^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ x^{2} }}=\frac{1}{\sqrt[3]{ x^{2} }}. \color{purple}{\frac{\sqrt[3]{ x }}{\sqrt[3]{ x }}} \\=\frac{\sqrt[3]{ x }}{x}\\---------------\)
4. \(\dfrac{y^{1}}{y^{\frac{-1}{4}}}\\= y^{ 1 - (\frac{-1}{4}) }= y^{\frac{5}{4}}\\=\sqrt[4]{ y^{5} }=|y|.\sqrt[4]{ y }\\---------------\)
5. \(\dfrac{y^{\frac{-1}{4}}}{y^{-1}}\\= y^{ \frac{-1}{4} - (-1) }= y^{\frac{3}{4}}\\=\sqrt[4]{ y^{3} }\\---------------\)
6. \(\dfrac{q^{-1}}{q^{\frac{2}{5}}}\\= q^{ -1 - \frac{2}{5} }= q^{\frac{-7}{5}}\\=\frac{1}{\sqrt[5]{ q^{7} }}\\=\frac{1}{q.\sqrt[5]{ q^{2} }}=\frac{1}{q.\sqrt[5]{ q^{2} }} \color{purple}{\frac{\sqrt[5]{ q^{3} }}{\sqrt[5]{ q^{3} }}} \\=\frac{\sqrt[5]{ q^{3} }}{q^{2}}\\---------------\)
7. \(\dfrac{x^{\frac{-3}{5}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{-3}{5} - (\frac{-1}{3}) }= x^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ x^{4} }}=\frac{1}{\sqrt[15]{ x^{4} }}. \color{purple}{\frac{\sqrt[15]{ x^{11} }}{\sqrt[15]{ x^{11} }}} \\=\frac{\sqrt[15]{ x^{11} }}{x}\\---------------\)
8. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{1}{6}}}\\= y^{ \frac{-1}{2} - \frac{1}{6} }= y^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ y^{2} }}=\frac{1}{\sqrt[3]{ y^{2} }}. \color{purple}{\frac{\sqrt[3]{ y }}{\sqrt[3]{ y }}} \\=\frac{\sqrt[3]{ y }}{y}\\---------------\)
9. \(\dfrac{a^{1}}{a^{-1}}\\= a^{ 1 - (-1) }= a^{2}\\\\---------------\)
10. \(\dfrac{a^{-1}}{a^{\frac{2}{3}}}\\= a^{ -1 - \frac{2}{3} }= a^{\frac{-5}{3}}\\=\frac{1}{\sqrt[3]{ a^{5} }}\\=\frac{1}{a.\sqrt[3]{ a^{2} }}=\frac{1}{a.\sqrt[3]{ a^{2} }} \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a^{2}}\\---------------\)
11. \(\dfrac{y^{\frac{-1}{3}}}{y^{\frac{5}{2}}}\\= y^{ \frac{-1}{3} - \frac{5}{2} }= y^{\frac{-17}{6}}\\=\frac{1}{\sqrt[6]{ y^{17} }}\\=\frac{1}{|y^{2}|.\sqrt[6]{ y^{5} }}=\frac{1}{|y^{2}|.\sqrt[6]{ y^{5} }} \color{purple}{\frac{\sqrt[6]{ y }}{\sqrt[6]{ y }}} \\=\frac{\sqrt[6]{ y }}{|y^{3}|}\\---------------\)
12. \(\dfrac{q^{\frac{2}{3}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{2}{3} - (\frac{-1}{3}) }= q^{1}\\\\---------------\)