Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{5}{3}}}\\= y^{ \frac{-1}{2} - \frac{5}{3} }= y^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ y^{13} }}\\=\frac{1}{|y^{2}|.\sqrt[6]{ y }}=\frac{1}{|y^{2}|.\sqrt[6]{ y }} \color{purple}{\frac{\sqrt[6]{ y^{5} }}{\sqrt[6]{ y^{5} }}} \\=\frac{\sqrt[6]{ y^{5} }}{|y^{3}|}\\---------------\)
2. \(\dfrac{a^{\frac{5}{3}}}{a^{\frac{-3}{5}}}\\= a^{ \frac{5}{3} - (\frac{-3}{5}) }= a^{\frac{34}{15}}\\=\sqrt[15]{ a^{34} }=a^{2}.\sqrt[15]{ a^{4} }\\---------------\)
3. \(\dfrac{x^{\frac{-1}{3}}}{x^{-1}}\\= x^{ \frac{-1}{3} - (-1) }= x^{\frac{2}{3}}\\=\sqrt[3]{ x^{2} }\\---------------\)
4. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{3}{4}}}\\= q^{ \frac{1}{2} - \frac{3}{4} }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)
5. \(\dfrac{x^{\frac{2}{3}}}{x^{1}}\\= x^{ \frac{2}{3} - 1 }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
6. \(\dfrac{a^{\frac{3}{5}}}{a^{\frac{-1}{5}}}\\= a^{ \frac{3}{5} - (\frac{-1}{5}) }= a^{\frac{4}{5}}\\=\sqrt[5]{ a^{4} }\\---------------\)
7. \(\dfrac{x^{\frac{1}{2}}}{x^{1}}\\= x^{ \frac{1}{2} - 1 }= x^{\frac{-1}{2}}\\=\frac{1}{ \sqrt{ x } }=\frac{1}{ \sqrt{ x } }. \color{purple}{\frac{ \sqrt{ x } }{ \sqrt{ x } }} \\=\frac{ \sqrt{ x } }{|x|}\\---------------\)
8. \(\dfrac{x^{\frac{4}{5}}}{x^{\frac{3}{5}}}\\= x^{ \frac{4}{5} - \frac{3}{5} }= x^{\frac{1}{5}}\\=\sqrt[5]{ x }\\---------------\)
9. \(\dfrac{a^{2}}{a^{1}}\\= a^{ 2 - 1 }= a^{1}\\\\---------------\)
10. \(\dfrac{q^{\frac{-5}{6}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{-5}{6} - (\frac{-1}{2}) }= q^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ q }}=\frac{1}{\sqrt[3]{ q }}. \color{purple}{\frac{\sqrt[3]{ q^{2} }}{\sqrt[3]{ q^{2} }}} \\=\frac{\sqrt[3]{ q^{2} }}{q}\\---------------\)
11. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{1}{2}}}\\= x^{ \frac{1}{3} - \frac{1}{2} }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
12. \(\dfrac{q^{1}}{q^{\frac{2}{3}}}\\= q^{ 1 - \frac{2}{3} }= q^{\frac{1}{3}}\\=\sqrt[3]{ q }\\---------------\)