Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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