Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-1}{2}}}{x^{-1}}\\= x^{ \frac{-1}{2} - (-1) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
2. \(\dfrac{a^{\frac{-5}{4}}}{a^{1}}\\= a^{ \frac{-5}{4} - 1 }= a^{\frac{-9}{4}}\\=\frac{1}{\sqrt[4]{ a^{9} }}\\=\frac{1}{|a^{2}|.\sqrt[4]{ a }}=\frac{1}{|a^{2}|.\sqrt[4]{ a }} \color{purple}{\frac{\sqrt[4]{ a^{3} }}{\sqrt[4]{ a^{3} }}} \\=\frac{\sqrt[4]{ a^{3} }}{|a^{3}|}\\---------------\)
3. \(\dfrac{y^{\frac{4}{3}}}{y^{\frac{5}{3}}}\\= y^{ \frac{4}{3} - \frac{5}{3} }= y^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ y }}=\frac{1}{\sqrt[3]{ y }}. \color{purple}{\frac{\sqrt[3]{ y^{2} }}{\sqrt[3]{ y^{2} }}} \\=\frac{\sqrt[3]{ y^{2} }}{y}\\---------------\)
4. \(\dfrac{a^{1}}{a^{\frac{-4}{5}}}\\= a^{ 1 - (\frac{-4}{5}) }= a^{\frac{9}{5}}\\=\sqrt[5]{ a^{9} }=a.\sqrt[5]{ a^{4} }\\---------------\)
5. \(\dfrac{q^{\frac{5}{4}}}{q^{\frac{-1}{5}}}\\= q^{ \frac{5}{4} - (\frac{-1}{5}) }= q^{\frac{29}{20}}\\=\sqrt[20]{ q^{29} }=|q|.\sqrt[20]{ q^{9} }\\---------------\)
6. \(\dfrac{x^{\frac{1}{3}}}{x^{\frac{3}{5}}}\\= x^{ \frac{1}{3} - \frac{3}{5} }= x^{\frac{-4}{15}}\\=\frac{1}{\sqrt[15]{ x^{4} }}=\frac{1}{\sqrt[15]{ x^{4} }}. \color{purple}{\frac{\sqrt[15]{ x^{11} }}{\sqrt[15]{ x^{11} }}} \\=\frac{\sqrt[15]{ x^{11} }}{x}\\---------------\)
7. \(\dfrac{a^{\frac{1}{3}}}{a^{\frac{-1}{2}}}\\= a^{ \frac{1}{3} - (\frac{-1}{2}) }= a^{\frac{5}{6}}\\=\sqrt[6]{ a^{5} }\\---------------\)
8. \(\dfrac{y^{\frac{-3}{5}}}{y^{\frac{1}{3}}}\\= y^{ \frac{-3}{5} - \frac{1}{3} }= y^{\frac{-14}{15}}\\=\frac{1}{\sqrt[15]{ y^{14} }}=\frac{1}{\sqrt[15]{ y^{14} }}. \color{purple}{\frac{\sqrt[15]{ y }}{\sqrt[15]{ y }}} \\=\frac{\sqrt[15]{ y }}{y}\\---------------\)
9. \(\dfrac{q^{\frac{3}{2}}}{q^{\frac{-4}{3}}}\\= q^{ \frac{3}{2} - (\frac{-4}{3}) }= q^{\frac{17}{6}}\\=\sqrt[6]{ q^{17} }=|q^{2}|.\sqrt[6]{ q^{5} }\\---------------\)
10. \(\dfrac{y^{\frac{2}{5}}}{y^{\frac{1}{3}}}\\= y^{ \frac{2}{5} - \frac{1}{3} }= y^{\frac{1}{15}}\\=\sqrt[15]{ y }\\---------------\)
11. \(\dfrac{x^{\frac{-1}{5}}}{x^{\frac{5}{4}}}\\= x^{ \frac{-1}{5} - \frac{5}{4} }= x^{\frac{-29}{20}}\\=\frac{1}{\sqrt[20]{ x^{29} }}\\=\frac{1}{|x|.\sqrt[20]{ x^{9} }}=\frac{1}{|x|.\sqrt[20]{ x^{9} }} \color{purple}{\frac{\sqrt[20]{ x^{11} }}{\sqrt[20]{ x^{11} }}} \\=\frac{\sqrt[20]{ x^{11} }}{|x^{2}|}\\---------------\)
12. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{2}{3}}}\\= q^{ \frac{1}{2} - \frac{2}{3} }= q^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ q }}=\frac{1}{\sqrt[6]{ q }}. \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q|}\\---------------\)