Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

1. \(\dfrac{q^{\frac{5}{4}}}{q^{\frac{2}{3}}}\\= q^{ \frac{5}{4} - \frac{2}{3} }= q^{\frac{7}{12}}\\=\sqrt[12]{ q^{7} }\\---------------\)
2. \(\dfrac{q^{\frac{-3}{2}}}{q^{\frac{-5}{3}}}\\= q^{ \frac{-3}{2} - (\frac{-5}{3}) }= q^{\frac{1}{6}}\\=\sqrt[6]{ q }\\---------------\)
3. \(\dfrac{x^{\frac{-2}{5}}}{x^{1}}\\= x^{ \frac{-2}{5} - 1 }= x^{\frac{-7}{5}}\\=\frac{1}{\sqrt[5]{ x^{7} }}\\=\frac{1}{x.\sqrt[5]{ x^{2} }}=\frac{1}{x.\sqrt[5]{ x^{2} }} \color{purple}{\frac{\sqrt[5]{ x^{3} }}{\sqrt[5]{ x^{3} }}} \\=\frac{\sqrt[5]{ x^{3} }}{x^{2}}\\---------------\)
4. \(\dfrac{y^{\frac{3}{5}}}{y^{\frac{3}{5}}}\\= y^{ \frac{3}{5} - \frac{3}{5} }= y^{0}\\=1\\---------------\)
5. \(\dfrac{q^{\frac{-3}{2}}}{q^{\frac{5}{3}}}\\= q^{ \frac{-3}{2} - \frac{5}{3} }= q^{\frac{-19}{6}}\\=\frac{1}{\sqrt[6]{ q^{19} }}\\=\frac{1}{|q^{3}|.\sqrt[6]{ q }}=\frac{1}{|q^{3}|.\sqrt[6]{ q }} \color{purple}{\frac{\sqrt[6]{ q^{5} }}{\sqrt[6]{ q^{5} }}} \\=\frac{\sqrt[6]{ q^{5} }}{|q^{4}|}\\---------------\)
6. \(\dfrac{x^{\frac{-1}{2}}}{x^{\frac{1}{4}}}\\= x^{ \frac{-1}{2} - \frac{1}{4} }= x^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ x^{3} }}=\frac{1}{\sqrt[4]{ x^{3} }}. \color{purple}{\frac{\sqrt[4]{ x }}{\sqrt[4]{ x }}} \\=\frac{\sqrt[4]{ x }}{|x|}\\---------------\)
7. \(\dfrac{a^{-1}}{a^{\frac{-1}{4}}}\\= a^{ -1 - (\frac{-1}{4}) }= a^{\frac{-3}{4}}\\=\frac{1}{\sqrt[4]{ a^{3} }}=\frac{1}{\sqrt[4]{ a^{3} }}. \color{purple}{\frac{\sqrt[4]{ a }}{\sqrt[4]{ a }}} \\=\frac{\sqrt[4]{ a }}{|a|}\\---------------\)
8. \(\dfrac{y^{\frac{5}{2}}}{y^{\frac{2}{3}}}\\= y^{ \frac{5}{2} - \frac{2}{3} }= y^{\frac{11}{6}}\\=\sqrt[6]{ y^{11} }=|y|.\sqrt[6]{ y^{5} }\\---------------\)
9. \(\dfrac{y^{\frac{-1}{2}}}{y^{\frac{-5}{6}}}\\= y^{ \frac{-1}{2} - (\frac{-5}{6}) }= y^{\frac{1}{3}}\\=\sqrt[3]{ y }\\---------------\)
10. \(\dfrac{x^{\frac{-3}{5}}}{x^{\frac{1}{5}}}\\= x^{ \frac{-3}{5} - \frac{1}{5} }= x^{\frac{-4}{5}}\\=\frac{1}{\sqrt[5]{ x^{4} }}=\frac{1}{\sqrt[5]{ x^{4} }}. \color{purple}{\frac{\sqrt[5]{ x }}{\sqrt[5]{ x }}} \\=\frac{\sqrt[5]{ x }}{x}\\---------------\)
11. \(\dfrac{a^{\frac{1}{3}}}{a^{1}}\\= a^{ \frac{1}{3} - 1 }= a^{\frac{-2}{3}}\\=\frac{1}{\sqrt[3]{ a^{2} }}=\frac{1}{\sqrt[3]{ a^{2} }}. \color{purple}{\frac{\sqrt[3]{ a }}{\sqrt[3]{ a }}} \\=\frac{\sqrt[3]{ a }}{a}\\---------------\)
12. \(\dfrac{y^{\frac{3}{5}}}{y^{\frac{-5}{4}}}\\= y^{ \frac{3}{5} - (\frac{-5}{4}) }= y^{\frac{37}{20}}\\=\sqrt[20]{ y^{37} }=|y|.\sqrt[20]{ y^{17} }\\---------------\)