Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{y^{\frac{3}{2}}}{y^{1}}\\= y^{ \frac{3}{2} - 1 }= y^{\frac{1}{2}}\\= \sqrt{ y } \\---------------\)
2. \(\dfrac{a^{\frac{2}{3}}}{a^{\frac{2}{5}}}\\= a^{ \frac{2}{3} - \frac{2}{5} }= a^{\frac{4}{15}}\\=\sqrt[15]{ a^{4} }\\---------------\)
3. \(\dfrac{a^{\frac{2}{5}}}{a^{\frac{-5}{4}}}\\= a^{ \frac{2}{5} - (\frac{-5}{4}) }= a^{\frac{33}{20}}\\=\sqrt[20]{ a^{33} }=|a|.\sqrt[20]{ a^{13} }\\---------------\)
4. \(\dfrac{x^{1}}{x^{\frac{-1}{5}}}\\= x^{ 1 - (\frac{-1}{5}) }= x^{\frac{6}{5}}\\=\sqrt[5]{ x^{6} }=x.\sqrt[5]{ x }\\---------------\)
5. \(\dfrac{y^{\frac{1}{6}}}{y^{\frac{1}{4}}}\\= y^{ \frac{1}{6} - \frac{1}{4} }= y^{\frac{-1}{12}}\\=\frac{1}{\sqrt[12]{ y }}=\frac{1}{\sqrt[12]{ y }}. \color{purple}{\frac{\sqrt[12]{ y^{11} }}{\sqrt[12]{ y^{11} }}} \\=\frac{\sqrt[12]{ y^{11} }}{|y|}\\---------------\)
6. \(\dfrac{q^{\frac{-3}{4}}}{q^{\frac{-1}{2}}}\\= q^{ \frac{-3}{4} - (\frac{-1}{2}) }= q^{\frac{-1}{4}}\\=\frac{1}{\sqrt[4]{ q }}=\frac{1}{\sqrt[4]{ q }}. \color{purple}{\frac{\sqrt[4]{ q^{3} }}{\sqrt[4]{ q^{3} }}} \\=\frac{\sqrt[4]{ q^{3} }}{|q|}\\---------------\)
7. \(\dfrac{a^{\frac{-1}{2}}}{a^{-1}}\\= a^{ \frac{-1}{2} - (-1) }= a^{\frac{1}{2}}\\= \sqrt{ a } \\---------------\)
8. \(\dfrac{q^{\frac{-1}{3}}}{q^{\frac{5}{4}}}\\= q^{ \frac{-1}{3} - \frac{5}{4} }= q^{\frac{-19}{12}}\\=\frac{1}{\sqrt[12]{ q^{19} }}\\=\frac{1}{|q|.\sqrt[12]{ q^{7} }}=\frac{1}{|q|.\sqrt[12]{ q^{7} }} \color{purple}{\frac{\sqrt[12]{ q^{5} }}{\sqrt[12]{ q^{5} }}} \\=\frac{\sqrt[12]{ q^{5} }}{|q^{2}|}\\---------------\)
9. \(\dfrac{q^{\frac{-2}{5}}}{q^{\frac{4}{3}}}\\= q^{ \frac{-2}{5} - \frac{4}{3} }= q^{\frac{-26}{15}}\\=\frac{1}{\sqrt[15]{ q^{26} }}\\=\frac{1}{q.\sqrt[15]{ q^{11} }}=\frac{1}{q.\sqrt[15]{ q^{11} }} \color{purple}{\frac{\sqrt[15]{ q^{4} }}{\sqrt[15]{ q^{4} }}} \\=\frac{\sqrt[15]{ q^{4} }}{q^{2}}\\---------------\)
10. \(\dfrac{a^{\frac{-4}{3}}}{a^{\frac{-5}{2}}}\\= a^{ \frac{-4}{3} - (\frac{-5}{2}) }= a^{\frac{7}{6}}\\=\sqrt[6]{ a^{7} }=|a|.\sqrt[6]{ a }\\---------------\)
11. \(\dfrac{q^{\frac{2}{5}}}{q^{\frac{5}{6}}}\\= q^{ \frac{2}{5} - \frac{5}{6} }= q^{\frac{-13}{30}}\\=\frac{1}{\sqrt[30]{ q^{13} }}=\frac{1}{\sqrt[30]{ q^{13} }}. \color{purple}{\frac{\sqrt[30]{ q^{17} }}{\sqrt[30]{ q^{17} }}} \\=\frac{\sqrt[30]{ q^{17} }}{|q|}\\---------------\)
12. \(\dfrac{q^{\frac{1}{3}}}{q^{\frac{5}{2}}}\\= q^{ \frac{1}{3} - \frac{5}{2} }= q^{\frac{-13}{6}}\\=\frac{1}{\sqrt[6]{ q^{13} }}\\=\frac{1}{|q^{2}|.\sqrt[6]{ q }}=\frac{1}{|q^{2}|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{3}|}\\---------------\)