Quotiënt zelfde grondtal

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Werk uit m.b.v. de rekenregels

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

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Werk uit m.b.v. de rekenregels

Verbetersleutel

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