Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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