Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{x^{\frac{1}{4}}}{x^{\frac{-2}{3}}}\\= x^{ \frac{1}{4} - (\frac{-2}{3}) }= x^{\frac{11}{12}}\\=\sqrt[12]{ x^{11} }\\---------------\)
2. \(\dfrac{x^{-1}}{x^{1}}\\= x^{ -1 - 1 }= x^{-2}\\=\frac{1}{x^{2}}\\---------------\)
3. \(\dfrac{q^{\frac{-1}{5}}}{q^{1}}\\= q^{ \frac{-1}{5} - 1 }= q^{\frac{-6}{5}}\\=\frac{1}{\sqrt[5]{ q^{6} }}\\=\frac{1}{q.\sqrt[5]{ q }}=\frac{1}{q.\sqrt[5]{ q }} \color{purple}{\frac{\sqrt[5]{ q^{4} }}{\sqrt[5]{ q^{4} }}} \\=\frac{\sqrt[5]{ q^{4} }}{q^{2}}\\---------------\)
4. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{5}{2}}}\\= q^{ \frac{2}{5} - \frac{5}{2} }= q^{\frac{-21}{10}}\\=\frac{1}{\sqrt[10]{ q^{21} }}\\=\frac{1}{|q^{2}|.\sqrt[10]{ q }}=\frac{1}{|q^{2}|.\sqrt[10]{ q }} \color{purple}{\frac{\sqrt[10]{ q^{9} }}{\sqrt[10]{ q^{9} }}} \\=\frac{\sqrt[10]{ q^{9} }}{|q^{3}|}\\---------------\)
5. \(\dfrac{y^{\frac{-5}{3}}}{y^{\frac{3}{4}}}\\= y^{ \frac{-5}{3} - \frac{3}{4} }= y^{\frac{-29}{12}}\\=\frac{1}{\sqrt[12]{ y^{29} }}\\=\frac{1}{|y^{2}|.\sqrt[12]{ y^{5} }}=\frac{1}{|y^{2}|.\sqrt[12]{ y^{5} }} \color{purple}{\frac{\sqrt[12]{ y^{7} }}{\sqrt[12]{ y^{7} }}} \\=\frac{\sqrt[12]{ y^{7} }}{|y^{3}|}\\---------------\)
6. \(\dfrac{x^{\frac{1}{5}}}{x^{\frac{3}{4}}}\\= x^{ \frac{1}{5} - \frac{3}{4} }= x^{\frac{-11}{20}}\\=\frac{1}{\sqrt[20]{ x^{11} }}=\frac{1}{\sqrt[20]{ x^{11} }}. \color{purple}{\frac{\sqrt[20]{ x^{9} }}{\sqrt[20]{ x^{9} }}} \\=\frac{\sqrt[20]{ x^{9} }}{|x|}\\---------------\)
7. \(\dfrac{a^{2}}{a^{1}}\\= a^{ 2 - 1 }= a^{1}\\\\---------------\)
8. \(\dfrac{x^{\frac{-5}{2}}}{x^{\frac{1}{3}}}\\= x^{ \frac{-5}{2} - \frac{1}{3} }= x^{\frac{-17}{6}}\\=\frac{1}{\sqrt[6]{ x^{17} }}\\=\frac{1}{|x^{2}|.\sqrt[6]{ x^{5} }}=\frac{1}{|x^{2}|.\sqrt[6]{ x^{5} }} \color{purple}{\frac{\sqrt[6]{ x }}{\sqrt[6]{ x }}} \\=\frac{\sqrt[6]{ x }}{|x^{3}|}\\---------------\)
9. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{-1}{3}}}\\= q^{ \frac{-1}{3} - (\frac{-1}{3}) }= q^{0}\\=1\\---------------\)
10. \(\dfrac{y^{\frac{5}{4}}}{y^{\frac{-3}{2}}}\\= y^{ \frac{5}{4} - (\frac{-3}{2}) }= y^{\frac{11}{4}}\\=\sqrt[4]{ y^{11} }=|y^{2}|.\sqrt[4]{ y^{3} }\\---------------\)
11. \(\dfrac{x^{\frac{3}{5}}}{x^{\frac{5}{4}}}\\= x^{ \frac{3}{5} - \frac{5}{4} }= x^{\frac{-13}{20}}\\=\frac{1}{\sqrt[20]{ x^{13} }}=\frac{1}{\sqrt[20]{ x^{13} }}. \color{purple}{\frac{\sqrt[20]{ x^{7} }}{\sqrt[20]{ x^{7} }}} \\=\frac{\sqrt[20]{ x^{7} }}{|x|}\\---------------\)
12. \(\dfrac{q^{\frac{1}{2}}}{q^{\frac{3}{4}}}\\= q^{ \frac{1}{2} - \frac{3}{4} }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)