Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{-3}{4}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{-3}{4} - (\frac{-1}{3}) }= x^{\frac{-5}{12}}\\=\frac{1}{\sqrt[12]{ x^{5} }}=\frac{1}{\sqrt[12]{ x^{5} }}. \color{purple}{\frac{\sqrt[12]{ x^{7} }}{\sqrt[12]{ x^{7} }}} \\=\frac{\sqrt[12]{ x^{7} }}{|x|}\\---------------\)
2. \(\dfrac{q^{\frac{3}{5}}}{q^{\frac{3}{2}}}\\= q^{ \frac{3}{5} - \frac{3}{2} }= q^{\frac{-9}{10}}\\=\frac{1}{\sqrt[10]{ q^{9} }}=\frac{1}{\sqrt[10]{ q^{9} }}. \color{purple}{\frac{\sqrt[10]{ q }}{\sqrt[10]{ q }}} \\=\frac{\sqrt[10]{ q }}{|q|}\\---------------\)
3. \(\dfrac{q^{\frac{-5}{4}}}{q^{\frac{2}{3}}}\\= q^{ \frac{-5}{4} - \frac{2}{3} }= q^{\frac{-23}{12}}\\=\frac{1}{\sqrt[12]{ q^{23} }}\\=\frac{1}{|q|.\sqrt[12]{ q^{11} }}=\frac{1}{|q|.\sqrt[12]{ q^{11} }} \color{purple}{\frac{\sqrt[12]{ q }}{\sqrt[12]{ q }}} \\=\frac{\sqrt[12]{ q }}{|q^{2}|}\\---------------\)
4. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{-4}{5}}}\\= y^{ \frac{5}{2} - (\frac{-4}{5}) }= y^{\frac{33}{10}}\\=\sqrt[10]{ y^{33} }=|y^{3}|.\sqrt[10]{ y^{3} }\\---------------\)
5. \(\dfrac{x^{\frac{-2}{3}}}{x^{\frac{-1}{3}}}\\= x^{ \frac{-2}{3} - (\frac{-1}{3}) }= x^{\frac{-1}{3}}\\=\frac{1}{\sqrt[3]{ x }}=\frac{1}{\sqrt[3]{ x }}. \color{purple}{\frac{\sqrt[3]{ x^{2} }}{\sqrt[3]{ x^{2} }}} \\=\frac{\sqrt[3]{ x^{2} }}{x}\\---------------\)
6. \(\dfrac{y^{\frac{3}{4}}}{y^{\frac{1}{4}}}\\= y^{ \frac{3}{4} - \frac{1}{4} }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
7. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{1}{5}}}\\= x^{ \frac{1}{2} - \frac{1}{5} }= x^{\frac{3}{10}}\\=\sqrt[10]{ x^{3} }\\---------------\)
8. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{5}{4}}}\\= x^{ \frac{-1}{3} - \frac{5}{4} }= x^{\frac{-19}{12}}\\=\frac{1}{\sqrt[12]{ x^{19} }}\\=\frac{1}{|x|.\sqrt[12]{ x^{7} }}=\frac{1}{|x|.\sqrt[12]{ x^{7} }} \color{purple}{\frac{\sqrt[12]{ x^{5} }}{\sqrt[12]{ x^{5} }}} \\=\frac{\sqrt[12]{ x^{5} }}{|x^{2}|}\\---------------\)
9. \(\dfrac{q^{\frac{-3}{4}}}{q^{\frac{4}{5}}}\\= q^{ \frac{-3}{4} - \frac{4}{5} }= q^{\frac{-31}{20}}\\=\frac{1}{\sqrt[20]{ q^{31} }}\\=\frac{1}{|q|.\sqrt[20]{ q^{11} }}=\frac{1}{|q|.\sqrt[20]{ q^{11} }} \color{purple}{\frac{\sqrt[20]{ q^{9} }}{\sqrt[20]{ q^{9} }}} \\=\frac{\sqrt[20]{ q^{9} }}{|q^{2}|}\\---------------\)
10. \(\dfrac{y^{1}}{y^{\frac{2}{3}}}\\= y^{ 1 - \frac{2}{3} }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
11. \(\dfrac{x^{\frac{-1}{3}}}{x^{\frac{-1}{5}}}\\= x^{ \frac{-1}{3} - (\frac{-1}{5}) }= x^{\frac{-2}{15}}\\=\frac{1}{\sqrt[15]{ x^{2} }}=\frac{1}{\sqrt[15]{ x^{2} }}. \color{purple}{\frac{\sqrt[15]{ x^{13} }}{\sqrt[15]{ x^{13} }}} \\=\frac{\sqrt[15]{ x^{13} }}{x}\\---------------\)
12. \(\dfrac{y^{\frac{5}{6}}}{y^{\frac{-1}{3}}}\\= y^{ \frac{5}{6} - (\frac{-1}{3}) }= y^{\frac{7}{6}}\\=\sqrt[6]{ y^{7} }=|y|.\sqrt[6]{ y }\\---------------\)