Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{-2}{3}}}{q^{\frac{1}{5}}}\\= q^{ \frac{-2}{3} - \frac{1}{5} }= q^{\frac{-13}{15}}\\=\frac{1}{\sqrt[15]{ q^{13} }}=\frac{1}{\sqrt[15]{ q^{13} }}. \color{purple}{\frac{\sqrt[15]{ q^{2} }}{\sqrt[15]{ q^{2} }}} \\=\frac{\sqrt[15]{ q^{2} }}{q}\\---------------\)
2. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{3}{5}}}\\= x^{ \frac{1}{2} - \frac{3}{5} }= x^{\frac{-1}{10}}\\=\frac{1}{\sqrt[10]{ x }}=\frac{1}{\sqrt[10]{ x }}. \color{purple}{\frac{\sqrt[10]{ x^{9} }}{\sqrt[10]{ x^{9} }}} \\=\frac{\sqrt[10]{ x^{9} }}{|x|}\\---------------\)
3. \(\dfrac{a^{2}}{a^{\frac{3}{5}}}\\= a^{ 2 - \frac{3}{5} }= a^{\frac{7}{5}}\\=\sqrt[5]{ a^{7} }=a.\sqrt[5]{ a^{2} }\\---------------\)
4. \(\dfrac{y^{\frac{-5}{4}}}{y^{\frac{4}{3}}}\\= y^{ \frac{-5}{4} - \frac{4}{3} }= y^{\frac{-31}{12}}\\=\frac{1}{\sqrt[12]{ y^{31} }}\\=\frac{1}{|y^{2}|.\sqrt[12]{ y^{7} }}=\frac{1}{|y^{2}|.\sqrt[12]{ y^{7} }} \color{purple}{\frac{\sqrt[12]{ y^{5} }}{\sqrt[12]{ y^{5} }}} \\=\frac{\sqrt[12]{ y^{5} }}{|y^{3}|}\\---------------\)
5. \(\dfrac{x^{\frac{3}{5}}}{x^{\frac{3}{4}}}\\= x^{ \frac{3}{5} - \frac{3}{4} }= x^{\frac{-3}{20}}\\=\frac{1}{\sqrt[20]{ x^{3} }}=\frac{1}{\sqrt[20]{ x^{3} }}. \color{purple}{\frac{\sqrt[20]{ x^{17} }}{\sqrt[20]{ x^{17} }}} \\=\frac{\sqrt[20]{ x^{17} }}{|x|}\\---------------\)
6. \(\dfrac{x^{\frac{-1}{2}}}{x^{-1}}\\= x^{ \frac{-1}{2} - (-1) }= x^{\frac{1}{2}}\\= \sqrt{ x } \\---------------\)
7. \(\dfrac{y^{\frac{-1}{6}}}{y^{\frac{-3}{5}}}\\= y^{ \frac{-1}{6} - (\frac{-3}{5}) }= y^{\frac{13}{30}}\\=\sqrt[30]{ y^{13} }\\---------------\)
8. \(\dfrac{a^{\frac{-5}{2}}}{a^{\frac{2}{3}}}\\= a^{ \frac{-5}{2} - \frac{2}{3} }= a^{\frac{-19}{6}}\\=\frac{1}{\sqrt[6]{ a^{19} }}\\=\frac{1}{|a^{3}|.\sqrt[6]{ a }}=\frac{1}{|a^{3}|.\sqrt[6]{ a }} \color{purple}{\frac{\sqrt[6]{ a^{5} }}{\sqrt[6]{ a^{5} }}} \\=\frac{\sqrt[6]{ a^{5} }}{|a^{4}|}\\---------------\)
9. \(\dfrac{q^{1}}{q^{\frac{1}{6}}}\\= q^{ 1 - \frac{1}{6} }= q^{\frac{5}{6}}\\=\sqrt[6]{ q^{5} }\\---------------\)
10. \(\dfrac{x^{\frac{1}{2}}}{x^{\frac{1}{5}}}\\= x^{ \frac{1}{2} - \frac{1}{5} }= x^{\frac{3}{10}}\\=\sqrt[10]{ x^{3} }\\---------------\)
11. \(\dfrac{x^{\frac{5}{6}}}{x^{1}}\\= x^{ \frac{5}{6} - 1 }= x^{\frac{-1}{6}}\\=\frac{1}{\sqrt[6]{ x }}=\frac{1}{\sqrt[6]{ x }}. \color{purple}{\frac{\sqrt[6]{ x^{5} }}{\sqrt[6]{ x^{5} }}} \\=\frac{\sqrt[6]{ x^{5} }}{|x|}\\---------------\)
12. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{-2}{3}}}\\= q^{ \frac{1}{3} - (\frac{-2}{3}) }= q^{1}\\\\---------------\)